A308055 a(1)=2; for n > 1, a(n) is the square root of the smallest square with a(n-1) as a prefix in base 10.

2, 5, 23, 48, 22, 15, 39, 63, 251, 501, 224, 474, 689, 2625, 5124, 22637, 47579, 68978, 83053, 28819, 53684, 2317, 4814, 6939, 26342, 51325, 71642, 84642, 290933, 1705676, 4129984, 20322363, 45080332, 67141889, 25911752, 16097128, 12687446, 35619442, 59682026

Offset: 1

Author

Sean Lipton, May 09 2019

Keywords

• nonn
• base
• easy
• look

Comments

The sequence contains the following squares: 315844, 289, 81, 9, and is eventually periodic. - Rémy Sigrist, Jul 13 2019

Examples

			a(1) = 2;
25 is the smallest square with 2 as a prefix;
a(2) = sqrt(25) = 5;
529 is the smallest square with 5 as a prefix;
a(3) = sqrt(529) = 23;
2304 is the smallest square with 23 as a prefix;
a(4) = sqrt(2304) = 48; etc.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..100
• Rémy Sigrist, PARI program for A308055

Crossrefs

Cf. A000290 (squares), A018851.

Programs

PARI

\\ See Links section.

Formula

From Rémy Sigrist, Jul 13 2019: (Start)

a(n+1) = A018851(a(n)).

a(n + 4) = a(n) for n >= 83. (End)

Extensions

a(31)-a(39) from Jon E. Schoenfield, May 10 2019

Comments corrected by Rémy Sigrist, Jul 13 2019