

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
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OFFSET

1,1


COMMENTS

As JeanPaul 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[#bwanted+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



