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

1,1

Comments

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]

Links

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

Example

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

Mathematica

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

Prog

(PARI) { 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
(PARI) 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

Crossrefs

Cf. A082026, A308170.

Sequence in context: A064853 A177148 A188739 * A265287 A329477 A257701

Adjacent sequences: A308168 A308169 A308170 * A308172 A308173 A308174

Keyword

nonn,base

Author

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

Extensions

More terms from Rémy Sigrist, May 15 2019

Status

approved