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A176774 Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal number. 10
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

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-Fran├žois 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

Cf. A090466, A090467.

Sequence in context: A123901 A214682 A093395 * A126352 A094758 A283971

Adjacent sequences:  A176771 A176772 A176773 * A176775 A176776 A176777

KEYWORD

nonn

AUTHOR

Max Alekseyev, Apr 25 2010

STATUS

approved

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Last modified August 18 14:09 EDT 2017. Contains 290720 sequences.