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A100251
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The square root of A100252; the index of the least square number greater than 1 that is also an n-gonal number, or 0 if none exists.
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7
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6, 2, 99, 35, 9, 15, 3, 0, 14, 8, 6, 21, 55, 4, 133, 10, 22, 0, 51, 27, 261, 15, 5, 85, 161, 9, 35, 451, 21, 33, 69, 14, 124, 6, 44, 715, 28, 24, 7421, 217, 34, 16, 23001, 54, 1065, 36, 7, 76, 156, 0, 245
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Let j be the smallest integer for which 1+(1+1*n)+(1+2*n)+... +(1+j*n)=k^2=s. Then a(n)=k; if no such j exists, then a(n)=0. Basis for sequence is shortest arithmetic series with initial term 1 and difference n that sums to a perfect square.
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FORMULA
| 1+(1+1*n)+(1+2*n)+...+(1+A100254(n)*n)= 1+(1+1*n)+(1+2*n)+...+A100253(n)=a(n)^2=A100252(n)
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EXAMPLE
| a(3)=99 since 1 + 4 + 7 +...+ (1+80*3)= 99^2 = 9801 and no other arithmetic series with initial term 1, difference 3 and fewer terms sums to a perfect square.
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MATHEMATICA
| NgonIndex[n_, v_] := (-4 + n + Sqrt[16 - 8*n + n^2 - 16*v + 8*n*v])/(n - 2)/2; Table[k = 2; While[sqr = k^2; i = NgonIndex[n, sqr]; k < 25000 && ! IntegerQ[i], k++]; If[k == 25000, k = sqr = i = 0]; k, {n, 3, 64}] - T. D. Noe, Apr 19 2011
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CROSSREFS
| Sequence in context: A201229 A038256 A192355 * A020339 A154738 A195738
Adjacent sequences: A100248 A100249 A100250 * A100252 A100253 A100254
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KEYWORD
| nonn
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AUTHOR
| Charlie Marion (charliemath(AT)optonline.net), Nov 21 2004
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