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

1,1

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..100

Rémy Sigrist, PARI program for A308055

Formula

From Rémy Sigrist, Jul 13 2019: (Begin)

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

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

(End)

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000290 (squares), A018851.

Sequence in context: A175444 A233443 A156314 * A173396 A023186 A023188

Adjacent sequences: A308052 A308053 A308054 * A308056 A308057 A308058

Keyword

nonn,base,easy,look

Author

Sean Lipton, May 09 2019

Extensions

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

Comments corrected by Rémy Sigrist, Jul 13 2019

Status

approved