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 A061588 a(1) = 2, a(n) = number obtained by replacing each digit of a(n-1) with its square. 4
 2, 4, 16, 136, 1936, 181936, 164181936, 13616164181936, 193613613616164181936, 1819361936193613613616164181936, 1641819361819361819361936193613613616164181936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES William Davidson, Introducing the peculiar 'Davidson Sequence', MathFest 2012. LINKS John Cerkan, Table of n, a(n) for n = 1..18 FORMULA From William Davidson, Aug 15 2012: (Start) For integer n > 5, a(n) = a(n-4)x10^(L(a(n-5))+L(a(n-1))) + a(n-5)x10^(L(a(n-1)))+a(n-1), where L(a(n)) is the number of digits in a(n). L(a(n)) = (W^(n-1)*[s1]^T)^T*[d]^T, with the 5 x 5 square matrix W = [(0 1 0 0 0) (0 0 1 0 0) (0 0 0 1 0) (0 0 0 0 1) ( 1 1 0 0 1)], [s1] = [1 2 3 4 6], [d] = [1 0 0 0 0], and ^T is the transformation of a matrix. To determine the starting integers of any a(n), for any integer n > 5, first let b = (((n + 2)mod(4)) + 2). Then using a(2), a(3), a(4), and a(5), any n > 5, a(n) begins with a(b). Let n = 100, b = 4, a(100) = 1936... (End) EXAMPLE After 136: the squares of 1, 3, 6 are 1, 9, 36 respectively hence the next term is 1936. a(11)=a(7)*10^L(a(6)+a(10))+a(6)*10^L(a(10))+a(10)      =13616164181936*10^55 + 164181936*10^46 +       1641819361819361819361936193613613616164181936      =136161641819361641819361641819361819361819361936193613613616164181936 a(100)=1936...*10^L(a(96)+a(99))+136...*10^L(a(99))+136...936, where L(100) has approximately 2.74*10^17 digits. - William Davidson, Aug 15 2012 PROG (Python) def digits(n): .d=[] .while n>0: ..d.append(n%10) ..n=n//10 .return d def sqdig(n): .new=0 .num=digits(n) .spacing=0 .while num: ..k=num.pop(0) ..new+=(10**(spacing))*(k**2) ..if k>3: ...spacing+=1 ..spacing+=1 .return new def davidson(n): .i=2 .while n>1: ..i=sqdig(i) ..n-=1 .return i # David Nacin, Aug 19 2012 CROSSREFS Sequence in context: A217994 A174677 A073924 * A202360 A050472 A109457 Adjacent sequences:  A061585 A061586 A061587 * A061589 A061590 A061591 KEYWORD nonn,easy,base AUTHOR Amarnath Murthy, May 13 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org) and Asher Natan Auel (auela(AT)reed.edu), May 15 2001. Corrected by Matthew Vandermast, Apr 23 2003 STATUS approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)