A176774 - OEIS

A176774

Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal number.

3, 4, 5, 3, 7, 8, 4, 3, 11, 5, 13, 14, 3, 4, 17, 7, 19, 20, 3, 5, 23, 9, 4, 26, 10, 3, 29, 11, 31, 32, 12, 7, 5, 3, 37, 38, 14, 8, 41, 15, 43, 44, 3, 9, 47, 17, 4, 50, 5, 10, 53, 19, 3, 56, 20, 11, 59, 21, 61, 62, 22, 4, 8, 3, 67, 68, 24, 5, 71, 25, 73, 74, 9, 14, 77, 3, 79, 80, 4, 15, 83

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OFFSET

3,1

COMMENTS

A176775(n) gives the index of n as a(n)-gonal number.

Since n is the second n-gonal number, a(n) <= n.

Furthermore, a(n)=n iff A176775(n)=2.

LINKS

Michel Marcus, Table of n, a(n) for n = 3..10000

Eric W. Weisstein, Polygonal Number. MathWorld.

EXAMPLE

a(12) = 5 since 12 is a pentagonal number, but not a square or triangular number. - Michael B. Porter, Jul 16 2016

MATHEMATICA

a[n_] := (m = 3; While[Reduce[k >= 1 && n == k (k (m - 2) - m + 4)/2, k, Integers] == False, m++]; m); Table[a[n], {n, 3, 100}] (* Jean-François Alcover, Sep 04 2016 *)

PROG

(PARI) a(n) = {k=3; while (! ispolygonal(n, k), k++); k; } \\ Michel Marcus, Mar 25 2015

(Python)

from __future__ import division

from gmpy2 import isqrt

def A176774(n):

k = (isqrt(8*n+1)-1)//2

while k >= 2:

a, b = divmod(2*(k*(k-2)+n), k*(k-1))

if not b:

return a

k -= 1 # Chai Wah Wu, Jul 28 2016