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A120744
Least k>0 such that a centered polygonal number nk(k+1)/2+1 is a perfect square; or -1 if no such number exists.
3
2, -1, 1, 3, 2, 7, 15, 1, 16, 8, 14, 4, 5, 15, 1, 2, 5, -1, 6, 3, 2, 39, 6, 1, 21, 7, 110, 3, 15, 7, 15, -1, 2, 8, 1, 4, 989, 8, 14, 2, 45, 15, 9, 4, 5, 335, 9, 1, 29, -1, 30, 15, 10, 415, 6, 2, 10, 32, 54, 3, 77, 55, 1, 5, 2, 7, 47750, 11, 15, 23, 47, -1, 48, 24, 16, 12, 5, 8, 2639, 1, 6720, 704, 38, 4, 2, 39, 505, 3, 13, 56, 9, 20, 13, 1631, 41
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Centered Polygonal Number
FORMULA
a(n) = -1 for n in A166259.
a(n) = 1 for n = k^2-1.
EXAMPLE
a(5) = 2 because A129556(2) = 2>1 and A129556(1) = 0<1.
KEYWORD
sign
AUTHOR
Alexander Adamchuk, Apr 26 2007
EXTENSIONS
Edited and b-file provided by Max Alekseyev, Jan 20 2010
STATUS
approved