A176873 Smallest possible integer m>=3 such that n is the sum of an m-gonal number and a k-gonal number for some k<=m.

3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 3, 5, 3, 3, 4, 3, 3, 3, 3, 3, 4, 5, 3, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 3, 5, 3, 3, 4, 3, 4, 4, 4, 3, 3, 3, 3, 4, 3, 3, 7, 5, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 5, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 3, 3, 4, 4

Offset: 0

Author

Max Alekseyev, Apr 27 2010

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A176774, A176874.

Programs

PARI

a(n)=if(ispolygonal(n,3) || ispolygonal(n-1,3), return(3)); for(m=3,if(n>5,(n+1)\2,4), my(i=2,t); while((t=n-(m-2)*binomial(i,2)-i)>=0, for(k=3,m, if(ispolygonal(t,k), return(m))); i++)) \\ Charles R Greathouse IV, Dec 11 2015

Formula

a(n) = min max(A176774(i),A176774(n-i)), where min is taken over i=0,1,...,n under the assumption that A176774(2) = +infinity.