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A135051 Pyramid game person numbers that have integer solutions. 1
7, 79, 191, 407, 631, 991, 1327, 1831, 2279, 2927, 3487, 4279, 4951, 5887, 6671, 7751, 8647, 9871, 10879, 12247, 13367, 14879, 16111, 17767, 19111, 20911, 22367, 24311, 25879, 27967, 29647, 31879, 33671, 36047, 37951, 40471, 42487, 45151, 47279, 50087, 52327, 55279, 57631, 60727, 63191, 66431, 69007, 72391, 75079, 78607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This result comes from looking for "perfect Pyramids" which is equivalent to finding m values that satisfy m(m + 1)/2 + 1 - n == 0, for each n value.

Integer solutions have the form such that 2*sqrt( -7 + 8*n), is an integer, and Mod[n - 7, 8], are equivalent to zero, simultaneously.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..468

FORMULA

From Colin Barker, Apr 30 2012: (Start)

Conjecture: a(n) = 9 - 2*(-1)^n + 4*(-8+(-1)^n)*n + 32*n^2.

Conjecture: G.f.: x*(7 + 72*x + 98*x^2 + 72*x^3 + 7*x^4)/((1-x)^3*(1+x)^2). (End)

MATHEMATICA

Flatten[Table[If[ IntegerQ[2*Sqrt[ -7 + 8*n]] && Mod[n - 7, 8] == 0, n, {}], {n, 1, 10000}]]

CROSSREFS

Sequence in context: A140613 A139945 A023285 * A201860 A176130 A014232

Adjacent sequences:  A135048 A135049 A135050 * A135052 A135053 A135054

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 31 2008

EXTENSIONS

a(19) to a(50) added and comments edited by G. C. Greubel, Sep 21 2016

STATUS

approved

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Last modified May 23 03:10 EDT 2019. Contains 323507 sequences. (Running on oeis4.)