

A101160


a(n) is the smallest integer j for which n+(n+1)+...+(n+j) is a square.


4



0, 2, 4, 0, 8, 10, 12, 14, 0, 18, 2, 1, 24, 26, 28, 0, 32, 4, 36, 38, 7, 42, 44, 1, 0, 2, 52, 54, 56, 58, 60, 8, 64, 66, 5, 0, 7, 74, 10, 1, 80, 82, 4, 86, 8, 12, 2, 94, 0, 98, 100, 17, 14, 106, 108, 110, 7, 9, 116, 1, 120, 23, 124, 0, 128
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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+a(n)) = n+(n+1)+...+A101159(n) = A101157(n)^2 = A101158(n).
a(n^2) = 0.  Michel Marcus, Jun 28 2013


EXAMPLE

a(11)=2 since j=2 is the smallest integer for which 11+...+11+j = 6^2 = 36 is a perfect square.


PROG

(PARI) a(n) = {j = 0; while(! issquare(sum(k=0, j, n+k)), j++); j; } \\ Michel Marcus, Sep 01 2013


CROSSREFS

Cf. A101157, A101158, A101159.
Sequence in context: A011166 A181274 A115341 * A103191 A324717 A295793
Adjacent sequences: A101157 A101158 A101159 * A101161 A101162 A101163


KEYWORD

nonn


AUTHOR

Charlie Marion, Dec 29 2004


EXTENSIONS

More terms from Michel Marcus, Jun 28 2013


STATUS

approved



