A340491 Number of n-digit numbers x such that rev(x^2) = rev(x)^2 and x does not contain any zero digits, where rev(x) is the digit reversal of x.

3, 6, 9, 11, 10, 7, 7, 1, 1

Offset: 1

Author

Sébastien Dumortier, Jan 10 2021

Keywords

• nonn
• base
• fini
• full

Comments

The number of solutions of rev(x^2) = rev(x)^2 increases but the solutions with a 0 don't. Any number with more than 9 digits can't be a solution, due to the development of x^2.

Examples

			The 7 solutions with 7 digits are 1111111, 1111112, 1111121, 1111211, 1121111, 1211111, 2111111.
		

Crossrefs

Cf. A098701 (number of solutions) and A085305 (the solutions), where digit 0 is not forbidden.

Cf. A004086 (digit reversal), A052382 (zeroless numbers).

Programs

PARI

isok(k) = my(d=digits(k)); vecmin(d) && (fromdigits(Vecrev(digits(k^2))) == fromdigits(Vecrev(d))^2);
a(n) = sum(k=10^(n-1), 10^n-1, isok(k)); \\ Michel Marcus, Jan 16 2021