A082026 -id:A082026 - cp's OEIS frontend

A308171 Limiting sequence of digits, read from the right, when starting with 5 we repeatedly replace each digit with its square (as in A308170).

5, 2, 4, 6, 1, 6, 3, 1, 6, 3, 9, 1, 6, 3, 9, 1, 8, 1, 6, 3, 9, 1, 8, 1, 4, 6, 1, 6, 3, 9, 1, 8, 1, 4, 6, 1, 6, 1, 6, 3, 1, 6, 3, 9, 1, 8, 1, 4, 6, 1, 6, 1, 6, 3, 1, 6, 3, 1, 6, 3, 9, 1, 6, 3, 9, 1, 8, 1, 4, 6, 1, 6, 1, 6, 3, 1, 6, 3, 1, 6, 3, 9, 1, 6, 3, 9, 1

Offset: 1

N. J. A. Sloane, May 15 2019, following a suggestion from Jeremy Gardiner

As Jean-Paul Allouche remarks on the SeqFan list, also the limiting sequence of the morphism 5 -> 52, 2 -> 4, 4 -> 61, 6 -> 63, 1 -> 1, 3 -> 9, 9 -> 18, 8 -> 46 over the alphabet {1..9} \ {7}, iterated on an initial value of 5. The digit 7 never occurs, and digits 2 and 5 only occur as a(1) and a(2). - M. F. Hasler, May 15 2019 [Corrected by N. J. A. Sloane, May 16 2019]

			Replacing each digit with its square, we get 5 -> 25 -> 425 -> 16425 -> 13616425 -> .... The final digits converge to ...16425, or read from the right, to this sequence: 5, 2, 4, 6, 1, ... - _M. F. Hasler_, May 15 2019

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Cf. A082026, A308170.

s = {5}; Do[s = Flatten[ Reverse@ IntegerDigits[#^2] & /@ s]; If[Length[s] > 100, s = Take[s, 100]], {100}]; s (* Giovanni Resta, Jul 03 2019 *)

{ wanted = 87; a = [5]; while (1, b = concat(apply(d -> if (d, digits(d^2), [0]), a)); if (#b > wanted, b = b[#b-wanted+1..#b]); if (a==b, break, a = b)); print (Vecrev(a)) } \\ Rémy Sigrist, May 15 2019

A308171_vec(N, a=[5])={while(a!=a=concat(apply(t->digits(t^2), if(#a>N, a[-N..-1], a))),); Vecrev(a[-N..-1])} \\ M. F. Hasler, May 15 2019

More terms from Rémy Sigrist, May 15 2019

A082027 a(1)=6; a(n) is concatenation of the squares of each digit of a(n-1), in order (in base 10).

Original entry on oeis.org

6, 36, 936, 81936, 64181936, 3616164181936, 93613613616164181936, 819361936193613613616164181936, 641819361819361819361936193613613616164181936

Offset: 1

Matthew Vandermast, Apr 01 2003

If m is a member of the sequence consisting of k base-10 digits, every member of the sequence greater than m is congruent to m modulo 10^k.

			a(4)=81936 because the squares of the digits of a(3)--namely, 9, 3 and 6--are 81, 9 and 36 respectively.

Cf. A061588, A082026.

NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]^2)]]&,6,10] (* Harvey P. Dale, Feb 28 2013 *)

cp's OEIS Frontend

A308171 Limiting sequence of digits, read from the right, when starting with 5 we repeatedly replace each digit with its square (as in A308170).

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