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A265153
a(1) = 15, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.
8
15, 21, 316, 969, 6996, 55401, 390625, 1827776, 2562500, 8273225, 37136225, 38371001, 43037561, 258421444, 792669636, 2928667041, 38512058944, 260125180889, 405701529401, 688085041025, 5890084946609, 22508111494025, 64017148660004, 537387232526336, 4166255964768676
OFFSET
1,1
EXAMPLE
a(3) is 316 since it is the least number greater than a(2)=21 which concatenated with 21 forms a perfect square, i.e., 21316 = 146^2.
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, 15, 24] (* after the algorithm of David W. Wilson in A090566 *)
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Dec 02 2015
STATUS
approved