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A176774 Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal 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 (list; graph; refs; listen; history; text; internal format)
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
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
CROSSREFS
Sequence in context: A349164 A214682 A093395 * A126352 A354998 A094758
KEYWORD
nonn
AUTHOR
Max Alekseyev, Apr 25 2010
STATUS
approved

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Last modified June 19 18:58 EDT 2024. Contains 373507 sequences. (Running on oeis4.)