A192934 Smallest square number starting with (at least) n identical digits.

1, 225, 22201, 5555449, 111112681, 3333330225, 555555566736, 2222222266944, 33333333393562596, 88888888888905609, 88888888888905609, 2222222222222640225, 2222222222222640225, 111111111111119590793871025, 5555555555555557064110500049, 11111111111111115805344390916

Offset: 1

Author

J. Lowell, Aug 25 2011

Keywords

• nonn
• base

Comments

Conjecture: total number of digits of a(n) is always 2*n-1.

This conjecture is false: length(a(6)) = 10 != 2*6-1 = 11.

Examples

			a(2) = 225 because none of 11, 22, 33, 44, 55, 66, 77, 88, 99, any integer from 110 to 119, or any integer from 220 to 224 is a square, but 15^2 = 225.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A119998, A119511.

Programs

PARI

a(n) = {if (n == 1, return (1)); ok = 0; i = 1; while (! ok, i++; d = digits(i^2, 10); if (#d >= n, ok = 1; for (k = 2, n, if (d[k] != d[1], ok = 0; break;);););); return (i^2);} \\ Michel Marcus, Jun 14 2013

Formula

a(n) = A119998(n)^2.

Extensions

More terms from Alois P. Heinz, Sep 02 2011