

A176948


a(n) is the smallest solution x to A176774(x)=n; a(n)=0 if this equation has no solution.


8



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

3,1


COMMENTS

A greedy inverse function to A176774.
Conjecture: For every n >= 4, except for n=6, there exists an ngonal number N which is not kgonal 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


LINKS

Chai Wah Wu, Table of n, a(n) for n = 3..10000


FORMULA

a(p) = p if p is any odd prime.


EXAMPLE

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


MAPLE

A139601 := proc(k, n) option remember ; n/2*( (k2)*nk+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:
seq(A176948(n), n=3..80) ; # R. J. Mathar, May 03 2010


MATHEMATICA

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}] (* JeanFrançois Alcover, Sep 04 2016 *)


CROSSREFS

Cf. A176744, A176747, A176775, A175873, A176874.
Sequence in context: A246667 A199066 A306584 * A113138 A010263 A011303
Adjacent sequences: A176945 A176946 A176947 * A176949 A176950 A176951


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Apr 29 2010


EXTENSIONS

More terms from R. J. Mathar, May 03 2010


STATUS

approved



