

A101158


Let j be the smallest integer for which n+(n+1)+...+(n+j) is a square; sequence gives the squares.


4



1, 9, 25, 4, 81, 121, 169, 225, 9, 361, 36, 25, 625, 729, 841, 16, 1089, 100, 1369, 1521, 196, 1849, 2025, 49, 25, 81, 2809, 3025, 3249, 3481, 3721, 324, 4225, 4489, 225, 36, 324, 5625, 484, 81, 6561, 6889, 225, 7569, 441, 676, 144, 9025, 49, 9801
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OFFSET

1,2


COMMENTS

Basis for sequence is shortest arithmetic sequence with initial term n and difference 1 that sums to a perfect square. Cf. A100251, A100252, A100253, A100254.


LINKS

Shawn A. Broyles, Table of n, a(n) for n = 1..1000


FORMULA

n+(n+1)+...+(n+A101160(n)) = n+(n+1)+...+A101159(n) = A101157(n)^2 = a(n).
a(n^2) = n^2.  Michel Marcus, Jun 28 2013


EXAMPLE

a(11)=36 since 11+12+13 = 36.


CROSSREFS

Cf. A101157, A101159, A101160.
Sequence in context: A121089 A050282 A096757 * A113496 A086531 A089091
Adjacent sequences: A101155 A101156 A101157 * A101159 A101160 A101161


KEYWORD

nonn


AUTHOR

Charlie Marion, Dec 29 2004


EXTENSIONS

a(21) corrected by Michel Marcus, Jun 29 2013


STATUS

approved



