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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

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

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*( (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:

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}] (* Jean-François 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

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Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)