A176775 Index of n as m-gonal number for the smallest possible m (=A176774(n)).

2, 2, 2, 3, 2, 2, 3, 4, 2, 3, 2, 2, 5, 4, 2, 3, 2, 2, 6, 4, 2, 3, 5, 2, 3, 7, 2, 3, 2, 2, 3, 4, 5, 8, 2, 2, 3, 4, 2, 3, 2, 2, 9, 4, 2, 3, 7, 2, 6, 4, 2, 3, 10, 2, 3, 4, 2, 3, 2, 2, 3, 8, 5, 11, 2, 2, 3, 7, 2, 3, 2, 2, 5, 4, 2, 12, 2, 2, 9, 4, 2, 3, 5, 2, 3, 4, 2, 3, 13, 8, 3, 4, 5, 6, 2, 2, 3, 10, 2, 3, 2, 2

Offset: 3

Author

Max Alekseyev, Apr 25 2010

Keywords

• nonn

Comments

a(n)=2 iff A176774(n)=n.

Links

• Michel Marcus, Table of n, a(n) for n = 3..10000
• Eric Weisstein's World of Mathematics, Polygonal Number.

Crossrefs

Cf. A176774.

Programs

PARI

f(n) = {k=3; while (! ispolygonal(n, k), k++); k; } \\ A176774
a(n) = my(m=f(n)); (m-4+sqrtint((m-4)^2+8*(m-2)*n)) / (2*m-4); \\ Michel Marcus, May 09 2021

Formula

a(n) = (m-4+sqrt((m-4)^2+8*(m-2)*n)) / (2*m-4), where m = A176774(n).