A265154 a(1) = 16, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.

16, 81, 225, 625, 681, 2100, 3889, 17841, 33121, 452049, 2561025, 9392964, 9776361, 69946276, 104857889, 232947041, 619807376, 729085444, 5435467076, 8236728484, 52686818481, 370961353041, 3290130736249, 4333224368201, 44310474545225, 67348431045184, 67835332918689

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Example

a(3) is 225 since it is the least number greater than a(2)=81 which concatenated with 81 forms a perfect square, i.e., 81225 = 285^2.

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, 16, 25] (* after the algorithm of David W. Wilson in A090566 *)

Crossrefs

Cf. A090566, A265147, A265148, A265149, A265150, A265151, A265152, A265153, A265155.

Sequence in context: A096020 A016898 A224135 * A268198 A212898 A212145

Adjacent sequences: A265151 A265152 A265153 * A265155 A265156 A265157

Keyword

nonn,base

Author

Robert G. Wilson v, Dec 02 2015

Status

approved