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A176948
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a(n) is the smallest solution x to A176774(x)=n; a(n)=0 if this equation has no solution.
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9
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3, 4, 5, 0, 7, 8, 24, 27, 11, 33, 13, 14, 42, 88, 17, 165, 19, 20, 60, 63, 23, 69, 72, 26, 255, 160, 29, 87, 31, 32, 315, 99, 102, 208, 37, 38, 114, 805, 41, 123, 43, 44, 132, 268, 47, 696, 475, 50, 150, 304, 53, 159, 162, 56, 168, 340, 59, 177, 61, 62, 615, 1309, 192, 388
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OFFSET
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3,1
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COMMENTS
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A greedy inverse function to A176774.
Conjecture: For every n >= 4, except for n=6, there exists an n-gonal number N which is not k-gonal for 3 <= k < n.
This means that the sequence contains only one 0: a(6)=0. For n=6 it is easy to prove that every hexagonal number (A000384) is also triangular (A000217), i.e., N does not exist. - Vladimir Shevelev, Apr 30 2010
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LINKS
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FORMULA
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a(p) = p if p is any odd prime.
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EXAMPLE
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For n=9, 24 is a nonagonal number, but not an octagonal number, heptagonal number, hexagonal number, etc. The smaller nonagonal number 9 is also a square number. Thus, a(9) = 24. - Michael B. Porter, Jul 16 2016
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MAPLE
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A139601 := proc(k, n) option remember ; n/2*( (k-2)*n-k+4) ; end proc:
A176774 := proc(n) option remember ; local k, m, pol ; for k from 3 do for m from 0 do pol := A139601(k, m) ; if pol = n then return k ; elif pol > n then break; end if; end do: end do: end proc:
A176948 := proc(n) if n = 6 then 0; else for x from 3 do if A176774(x)= n then return x ; end if; end do: end if; end proc:
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MATHEMATICA
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A176774[n_] := A176774[n] = (m = 3; While[Reduce[k >= 1 && n == k (k (m - 2) - m + 4)/2, k, Integers] == False, m++]; m); a[6] = 0; a[p_?PrimeQ] := p; a[n_] := (x = 3; While[A176774[x] != n, x++]; x); Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 3, 100}] (* Jean-François Alcover, Sep 04 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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