## Wednesday, January 13, 2016

### Happy Birthday Doc!

1/13/2016

Hey Doc,

In the square below choose one of the numbers and circle it.  Then cross out every number above it, below it, to the left of it or to the right of it.
From the numbers that are not circled or crossed out choose another number and circle it.  Then cross out every number above it, below it, to the left of it, or to the right of it.
 5 9 13 15 26 8 12 16 18 29 13 17 21 23 34 18 22 26 28 39 28 32 36 39 49
From the numbers that are not circled or crossed out choose another number and circle it.  Then cross out every number above it, below it, to the left of it, or to the right of it.
From the numbers that are not circled or crossed out choose another number and circle it.  Then cross out every number above it, below it, to the left of it, or to the right of it.
Now you should have only one number that is not circled or crossed out.  If you have more than one number to choose from – please start over (reprint the page).  If you have just one number left, go ahead and circle that number.  Now add up the five numbers you circled.  That is your Mathematological Lucky Number for today.
Then I can use that number (which is 115 – right? – just checking) to calculate your Magic Birthday Square.
Since your mathematological lucky number is 115 your Magic Birthday Square has to have a magic square constant of 115. Each row, each column and both diagonal have to add up to 115.  And there are some other, more complex patterns I have to incorporate too.

Give me a minute.

Or maybe a couple of minutes or may five minutes.

OK.
Hear is your Magic Birthday Square.
Check to make sure that every row, every column, and both diagonals add up to 115.  (Never mind – I already checked it.)
 1 13 19 82 20 81 2 12 80 17 15 3 14 4 79 18
Now check to see if the four corners add up to 115.
And check to see if the middle four numbers add up to 115.
And check to see if the date in the top row is actually your birthday.
If that date is wrong then you’re the wrong Doc – sorry to bother you.

David

## Friday, January 1, 2016

### New Sequence Numbers for 2016 - Happy New Year

1/01/2016

You know I am a fan of sequence numbers, and today seemed to be the right day to share these.

 Multiples of 2016: The digital expansion of the inverse of the sequence number 49,603,174,603,075,396,825,396,875 produces a sequence of the multiples of 2016, written in six digit strings, beginning with 0 * 2016 and continuing through 997,920 (which is 495 * 2016) before making an error. 1/49603174603075396825396875 = 0.00000 000000  002016  004032  006048  008064  010080  012096  014112  016128  018144  020160  022176  024192  026208  028224  030240  032256  034272  036288  038304  040320  042336  044352  046368  048384  050400  052416  054432  056448  058464  060480  062496  064512  066528  068544  070560  072576  074592  076608  078624  080640  082656  084672  086688  088704  090720  092736  094752  096768  098784  100800  102816  104832  106848  108864  110880  112896  114912  116928  118944  120960  122976  124992  127008  129024  131040  133056  135072  137088  139104  141120  143136  145152  147168  149184  151200  153216  155232  157248  159264  161280  163296  165312  167328  169344  171360  173376  175392  177408  179424  181440  183456  185472  187488  189504  191520  193536  195552  197568  199584  201600  203616  205632  207648  209664  211680  213696  215712  217728  219744  221760  223776  225792  227808  229824  231840  233856  235872  237888  239904  241920  243936  245952  247968  249984  252000  254016  256032  258048  260064  262080  264096  266112  268128  270144  272160  274176  276192  278208  280224  282240  284256  286272  288288  290304  292320  294336  296352  298368  300384  302400  304416  306432  308448  310464  312480  314496  316512  318528  320544  322560  324576  326592  328608  330624  332640  334656  336672  338688  340704  342720  344736  346752  348768  350784  352800  354816  356832  358848  360864  362880  364896  366912  368928  370944  372960  374976  376992  379008  381024  383040  385056  387072  389088  391104  393120  395136  397152  399168  401184  403200  405216  407232  409248  411264  413280  415296  417312  419328  421344  423360  425376  427392  429408  431424  433440  435456  437472  439488  441504  443520  445536  447552  449568  451584  453600  455616  457632  459648  461664  463680  465696  467712  469728  471744  473760  475776  477792  479808  481824 483840  485856  487872  489888  491904  493920  495936  497952  499968  501984  504000  506016  508032  510048  512064  514080  516096  518112  520128  522144  524160  526176  528192  530208  532224  534240  536256  538272  540288  542304  544320  546336  548352  550368  552384  554400  556416  558432  560448  562464  564480  566496  568512  570528  572544  574560  576576  578592  580608  582624  584640  586656  588672  590688  592704  594720 596736  598752  600768  602784  604800  606816  608832  610848  612864  614880  616896  618912  620928  622944  624960  626976  628992  631008  633024  635040  637056  639072  641088  643104  645120  647136  649152  651168  653184  655200  657216  659232  661248  663264  665280  667296  669312  671328  673344  675360  677376  679392  681408  683424  685440  687456  689472  691488  693504  695520  697536  699552  701568  703584  705600  707616  709632  711648  713664  715680  717696  719712  721728  723744  725760  727776  729792  731808  733824  735840  737856  739872  741888  743904  745920  747936  749952  751968  753984  756000  758016  760032  762048  764064  766080  768096  770112  772128  774144  776160  778176  780192  782208  784224  786240  788256  790272  792288  794304  796320  798336  800352  802368  804384  806400  808416  810432  812448  814464  816480  818496  820512  822528  824544  826560  828576  830592  832608  834624  836640  838656  840672  842688  844704  846720  848736  850752  852768  854784  856800  858816  860832  862848  864864  866880  868896  870912  872928  874944  876960  878976  880992  883008  885024  887040  889056  891072  893088  895104  897120  899136  901152  903168  905184  907200  909216  911232  913248  915264  917280  919296  921312  923328  925344  927360  929376  931392  933408  935424  937440  939456  941472  943488  945504  947520  949536  951552  953568  955584  957600  959616  961632  963648  965664  967680  969696  971712  973728  975744  977760  979776  981792  983808  985824  987840  989856  991872  993888  995904  997920 If you need to produce a list with more terms the sequence number 49,603,174,603,075,396,825,396,875 can be used.  It will write the terms in 12 digit sequences.  In theory, it would be accurate up to the 496,031,745th term, which would be 999,999,997,920, but I lack the computing power to produce this sequence.  I would need to be able to calculate the value of 1/49603174603075396825396875 to almost 6 billion digits past the decimal point.  It would take 340 cases of paper just to print the entire sequence.  I will leave this as an exercise for the reader to complete. David  “Pay no attention to the man behind the curtain.”

 A Sequence Number to show the Powers of 2016: The digital expansion of the inverse of 999,999,999,999,999,999,999,999,999,999,997,984 will produce a sequence of digits that show the powers of 2016, written in 36 digit strings, beginning with 20160, and accurate through 201610. 1/999999999999999999999999999999997984 = 0. 000000000000000000000000000000000001  000000000000000000000000000000002016  000000000000000000000000000004064256  000000000000000000000000008193540096  000000000000000000000016518176833536  000000000000000000033300644496408576  000000000000000067134099304759689216  000000000000135342344198395533459456  000000000272850165903965395454263296  000000550065934462394237235794804736  001108932923876186782267362326347778  … David

 A Special 2,0,1,6 Tetranacci Sequence Number for 2016: This is a special Tetranacci Sequence defined as : a(0) = a(1) = a(2) = 0, a(3) = 1, and when n>3 then a(n) = 2 * a(n-1) + 0 * a(n–2) + 1 * a(n-3) + 6 * a(n-4). The digital expansion of the inverse of the sequence number 9,999,999,999,999,997,999,999,999,999,999,999,999,999,999, 999,989,999,999,999,999,994 produces a digital sequence that shows the terms of the special Tetranacci Sequence defined in the paragraph above.  It will write the terms in 16 digit strings.  It is accurate to the 40th non-zero term. 1/999999999999999799999999999999999999999999999998999 9999999999994 = 0. 0000000000000000  0000000000000000  0000000000000000  0000000000000001  0000000000000002  0000000000000004  0000000000000009  0000000000000026  0000000000000068  0000000000000169  0000000000000418  0000000000001060  0000000000002697  0000000000006826  0000000000017220  0000000000043497  0000000000110002  0000000000278180  0000000000703177  0000000001777338  0000000004492868  0000000011357993  0000000028712386  0000000072581668  0000000183478537  0000000463817418  0000001172490820  0000002963950185  0000007492589010  0000018940573348  0000047880041801  0000121036373722  0000305968854852  0000773461191593  0001955239007714  0004942665112612  0012494604545929  0031585215249130  0079844529657156  0201839654535913  0510232151596530  1289820124344996  3260547081168841  … David