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A236444 Natural numbers not in A236019.

%I A236444 #18 Feb 12 2018 16:31:45
%S A236444 1,3,4,6,7,9,11,12,14,16,18,19,21,23,25,27,29,30,32,34,36,38,40,42,44,
%T A236444 45,47,49,51,53,55,57,59,61,63,65,67,68,70,72,74,76,78,80,82,84,86,88,
%U A236444 90,92,94,96,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129
%N A236444 Natural numbers not in A236019.
%C A236444 A236019(n+1) - A236019(n) = 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3,... . Only 2's and 3's ?
%C A236444 a(n+1) - a(n) = 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1,... . Only 2's and 1's ?
%C A236444 d(n) = A236019(n) - a(n) = -1, -1, 1, 2, 3, 4, 4, 5, 6, 6, 6, 7, 7,... .
%C A236444 Nondecreasing numbers?
%H A236444 Alois P. Heinz, <a href="/A236444/b236444.txt">Table of n, a(n) for n = 1..10000</a>
%e A236444 Irregular triangle by consecutive odds and evens.
%e A236444 1,   3,
%e A236444 4,   6,
%e A236444 7,   9, 11,
%e A236444 12, 14, 16, 18,
%e A236444 19, 21, 23, 25, 27, 29,
%e A236444 30, 32, 34, 36, 38, 40, 42, 44,
%e A236444 etc.
%e A236444 Hence the unknown sequence b(n)=2, 2, 3, 4, 6, 8, 12, 15,... .
%t A236444 $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; A236019 = Table[a[n], {n, 0, 100}] ; A236444 = Complement[Range[A236019 // Last], A236019] (* _Jean-François Alcover_, Dec 17 2014, after _Alois P. Heinz_ *)
%Y A236444 Complement of A236019.
%K A236444 nonn
%O A236444 1,2
%A A236444 _Paul Curtz_, Jan 26 2014
%E A236444 Offset corrected by _Michel Marcus_, Feb 12 2018