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A243091
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Least number k > n such that n concatenated with k is a perfect square.
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4
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1, 6, 5, 6, 9, 29, 25, 29, 41, 61, 24, 56, 25, 69, 44, 21, 81, 64, 49, 36, 25, 316, 201, 104, 336, 281, 244, 225, 224, 241, 276, 36, 49, 64, 81, 344, 100, 249, 44, 69, 96, 209, 436, 56, 89, 369, 225, 61, 400, 284, 176, 84, 441, 361, 76, 225, 169, 76, 564, 536, 84, 504, 500, 504, 516, 536
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OFFSET
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0,2
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COMMENTS
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Records occur at: 0, 1, 4, 5, 8, 9, 13, 16, 21, 24, 35, 42, 52, 58, 67, 75, 80, ..., . - Robert G. Wilson v, Nov 23 2015
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LINKS
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EXAMPLE
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a(1) = 6 since 6>1 and 16 = 4^2.
a(2) = 5 since 5>2 and 25 = 5^2.
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MATHEMATICA
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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) (10 x + 1) - 1] + 1)^2, 10^(d + 1)]]]; Array[f, 65] (* Robert G. Wilson v, Nov 23 2015, after the algorithm of David W. Wilson in A090566 *)
lnk[n_]:=Module[{k=n+1}, While[!IntegerQ[Sqrt[n 10^IntegerLength[k]+k]], k++]; k]; Array[lnk, 70, 0] (* Harvey P. Dale, Sep 01 2023 *)
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PROG
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(PARI) a(n)=s=Str(n); k=n+1; while(!issquare(eval(concat(s, Str(k)))), k++); return(k)
vector(100, n, a(n))
(PARI) A048761 = t->(sqrtint(t-1)+1)^2
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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