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

3,1

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.

Formula

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

Prog

(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

Crossrefs

Cf. A176774.

Sequence in context: A226056 A104011 A242879 * A175778 A357039 A226182

Adjacent sequences: A176772 A176773 A176774 * A176776 A176777 A176778

Keyword

nonn

Author

Max Alekseyev, Apr 25 2010

Status

approved