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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).

%I A308171 #29 Jul 09 2025 04:47:00
%S A308171 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,
%T A308171 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,
%U A308171 4,6,1,6,1,6,3,1,6,3,1,6,3,9,1,6,3,9,1
%N A308171 Limiting sequence of digits, read from the right, when starting with 5 we repeatedly replace each digit with its square (as in A308170).
%C A308171 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]
%H A308171 Rémy Sigrist, <a href="/A308171/b308171.txt">Table of n, a(n) for n = 1..25000</a>
%e A308171 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
%t A308171 s = {5}; Do[s = Flatten[ Reverse@ IntegerDigits[#^2] & /@ s]; If[Length[s] > 100, s = Take[s, 100]], {100}]; s (* _Giovanni Resta_, Jul 03 2019 *)
%o A308171 (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
%o A308171 (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
%Y A308171 Cf. A082026, A308170.
%K A308171 nonn,base
%O A308171 1,1
%A A308171 _N. J. A. Sloane_, May 15 2019, following a suggestion from _Jeremy Gardiner_
%E A308171 More terms from _Rémy Sigrist_, May 15 2019