A265148 a(1) = 4, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.

4, 9, 61, 504, 4516, 47504, 382025, 3975209, 33057329, 80214016, 454665681, 4507966404, 44168848384, 69005350809, 163894140625, 784386132324, 5954843762641, 7954794246144, 53996843222416, 69176076458289, 379510987739761, 1641640879622564, 7593632535763529, 31733339799107600

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

a(3) is 61 since it is the least number greater than a(2)=9 which concatenated with 9 forms a perfect square, i.e., 961 = 31^2.

Mathematica

f[n_] := Block[{x = n, d = 1 + Floor@ Log10@ n}, q = (Floor@ Sqrt[(10^d + 1) x] + 1)^2; If[q < (10^d) (x + 1), Mod[q, 10^d], Mod[(Floor@ Sqrt[(10^d)(10x + 1) - 1] + 1)^2, 10^(d + 1)] ]]; NestList[f, 4, 23] (* after the algorithm of David W. Wilson in A090566 *)

Crossrefs

Cf. A090566, A265147, A265149, A265150, A265151, A265152, A265153, A265154, A265155.

Sequence in context: A013571 A002942 A028908 * A220445 A360751 A073658

Adjacent sequences: A265145 A265146 A265147 * A265149 A265150 A265151

Keyword

nonn,base

Author

Robert G. Wilson v, Dec 02 2015

Status

approved