cp's OEIS Frontend

A283370 Minimal number of terms required to write n as sum of numbers in A000389 = { C(k,5); k=1,2,3,... } (with repetitions allowed).

%I A283370 #20 Jun 07 2025 09:23:41
%S A283370 0,1,2,3,4,5,1,2,3,4,5,6,2,3,4,5,6,7,3,4,5,1,2,3,4,5,6,2,3,4,5,6,7,3,
%T A283370 4,5,6,7,8,4,5,6,2,3,4,5,6,7,3,4,5,6,7,8,4,5,1,2,3,4,5,6,2,3,4,5,6,7,
%U A283370 3,4,5,6,7,8,4,5,6,2,3,4,5,6,7,3,4,5,6
%N A283370 Minimal number of terms required to write n as sum of numbers in A000389 = { C(k,5); k=1,2,3,... } (with repetitions allowed).
%C A283370 Analog, for A000389 = {C(n,5)}, of A061336 (for triangular numbers A000217 = {C(n,2)}), A104246 (for tetrahedral numbers A000292 = {C(n,3)}) and A283365 (for A000332 = {C(n,4)}).
%H A283370 R. J. Mathar, <a href="/A283370/b283370.txt">Table of n, a(n) for n = 0..10000</a>
%H A283370 Hyun Kwang Kim, <a href="https://doi.org/10.1090/S0002-9939-02-06710-2">On regular polytope numbers</a>, Proc. Amer. Math. Soc. 131 (2003), p. 65-75. DOI:10.1090/S0002-9939-02-06710-2.
%F A283370 a(n) <= 10 = a(220) for all n, according to Kim (2003, p. 74, first row of table "d = 5"), but this "numerical result" has no "* denoting exact values" (see Remark at end of paper), so it could be incorrect. [Disclaimer added by _M. F. Hasler_, Sep 22 2022]
%o A283370 (PARI) {a(n,k=5,M=9e9,N=n) = n>k || return(n); for(m=k,M,binomial(m,k)>n && (M=m) && break); M-- <= k && return(n); my(b=binomial(M,k),c=binomial(M-1,k),NN); forstep( nn=n\b,0,-1, if(N>NN=nn+a(n-nn*b,k,M,N),N=NN); n-(nn-1)*b >= (N-nn+1)*c && break); N}
%Y A283370 Cf. A000332 = {C(n,4)}; A061336 (analog for A000217), A104246 (analog for A000292), A283365 (analog for A000332).
%K A283370 nonn
%O A283370 0,3
%A A283370 _M. F. Hasler_, Mar 06 2017