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A236019 Smallest number having at least n partitions that contain at least n primes.

%I A236019 #30 Mar 19 2018 13:22:10
%S A236019 0,2,5,8,10,13,15,17,20,22,24,26,28,31,33,35,37,39,41,43,46,48,50,52,
%T A236019 54,56,58,60,62,64,66,69,71,73,75,77,79,81,83,85,87,89,91,93,95,98,
%U A236019 100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130
%N A236019 Smallest number having at least n partitions that contain at least n primes.
%H A236019 Alois P. Heinz, <a href="/A236019/b236019.txt">Table of n, a(n) for n = 0..10000</a>
%e A236019 a(4) = 10: [2,2,2,2,1,1], [2,2,2,2,2], [3,2,2,2,1], [3,3,2,2].
%p A236019 b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A236019      `if`(i<1, 0, b(n, i-1, t) +`if`(i>n, 0,
%p A236019       b(n-i, i, t -`if`(t>0 and isprime(i), 1, 0)))))
%p A236019     end:
%p A236019 a:= proc(n) option remember; local k;
%p A236019       for k from a(n-1) while b(k, k, n)<n do od; k
%p A236019     end: a(0):=0:
%p A236019 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jan 18 2014
%t A236019 $RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t - If[t>0 && PrimeQ[i], 1, 0]]]]]; a[n_] := a[n] = Module[{k}, For[k = a[n-1], b[k, k, n] < n, k++]; k]; a[0] = 0; Table[a[n], {n, 0, 61}] (* _Jean-François Alcover_, Jan 27 2014, after _Alois P. Heinz_ *)
%Y A236019 Cf. A000041, A002095, A235945, A236444 (complement).
%K A236019 nonn
%O A236019 0,2
%A A236019 _J. Stauduhar_, Jan 18 2014
%E A236019 More terms from _Alois P. Heinz_, Jan 18 2014