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 A176774 Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal number. 18
 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-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 Cf. A090466, A090467. Sequence in context: A349164 A214682 A093395 * A126352 A354998 A094758 Adjacent sequences: A176771 A176772 A176773 * A176775 A176776 A176777 KEYWORD nonn AUTHOR Max Alekseyev, Apr 25 2010 STATUS approved

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Last modified December 5 17:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)