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%I #24 Apr 29 2021 01:37:13
%S 3,4,5,0,7,8,24,27,11,33,13,14,42,88,17,165,19,20,60,63,23,69,72,26,
%T 255,160,29,87,31,32,315,99,102,208,37,38,114,805,41,123,43,44,132,
%U 268,47,696,475,50,150,304,53,159,162,56,168,340,59,177,61,62,615,1309,192,388
%N a(n) is the smallest solution x to A176774(x)=n; a(n)=0 if this equation has no solution.
%C A greedy inverse function to A176774.
%C 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.
%C 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
%H Chai Wah Wu, <a href="/A176948/b176948.txt">Table of n, a(n) for n = 3..10000</a>
%F a(p) = p if p is any odd prime.
%e 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
%p A139601 := proc(k,n) option remember ; n/2*( (k-2)*n-k+4) ; end proc:
%p 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:
%p 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:
%p seq(A176948(n),n=3..80) ; # _R. J. Mathar_, May 03 2010
%t 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 *)
%Y Cf. A176744, A176747, A176775, A175873, A176874.
%K nonn
%O 3,1
%A _Vladimir Shevelev_, Apr 29 2010
%E More terms from _R. J. Mathar_, May 03 2010
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