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A308171 Limiting sequence of digits, read from the right, when starting with 5 we repeatedly replace each digit with its square (as in A308170). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 14:29 EST 2021. Contains 340467 sequences. (Running on oeis4.)