

A176774


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


19



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 ngonal number, a(n) <= n.
Furthermore, a(n)=n iff A176775(n)=2.


LINKS



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}] (* JeanFrançois 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
k = (isqrt(8*n+1)1)//2
while k >= 2:
a, b = divmod(2*(k*(k2)+n), k*(k1))
if not b:
return a


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



