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A176774
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Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal number.
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19
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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
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3,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(12) = 5 since 12 is a pentagonal number, but not a square or triangular number. - Michael B. Porter, Jul 16 2016
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MATHEMATICA
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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 *)
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PROG
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(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*(k-2)+n), k*(k-1))
if not b:
return a
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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