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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. 2

%I #4 Dec 11 2015 08:57:35

%S 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,

%T 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,

%U 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

%N 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.

%H Charles R Greathouse IV, <a href="/A176873/b176873.txt">Table of n, a(n) for n = 0..10000</a>

%F 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.

%o (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

%Y Cf. A176774, A176874.

%K nonn

%O 0,1

%A _Max Alekseyev_, Apr 27 2010

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