A308170 Start with the number 7, repeatedly square every digit in place to get a new number; in the limit this process converges (reading from right to left) to the string shown here.

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, 6, 3, 9, 1, 8, 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, 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, 9

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

If we start with 3 or 9, we get the same sequence. If instead we start with 2, 4, 6, or 8 we get the same sequence but without the initial 1. If we start with 5 we get A308171. [Corrected by M. F. Hasler, May 15 2019]

Comment from Jean-Paul Allouche, May 15 2019: These sequences can be obtained in the order shown (that is, in the right-to-left order) by starting with 7 (say), and repeatedly applying the morphism on the alphabet {1,2,3,...,9} defined by 1 -> 1, 3 -> 9, 4 -> 61, 5 -> 52, 6 -> 63, 7 -> 94, 8 -> 46, 9 -> 18.

If we start with 1, application of the morphism will never change that initial sequence of length 1: this is the third fixed point of the morphism. - M. F. Hasler, May 15 2019

Examples

			The successive numbers that arise are
7
49
1681
136641
193636161
1819369361361
1641819368193619361
...
and reading from the right we see 1,6,3,9, ...
		

Links

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

Crossrefs

Cf. A048385, A061588, A082027, A308171.

Programs

PARI

{ wanted = 87; a = [7]; 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

A308170_vec(N,a=[9])={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

Extensions

More terms from Rémy Sigrist, May 15 2019