A236444 Natural numbers not in A236019.

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, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129

Offset: 1

Author

Paul Curtz, Jan 26 2014

Keywords

• nonn

Comments

A236019(n+1) - A236019(n) = 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3,... . Only 2's and 3's ?

a(n+1) - a(n) = 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1,... . Only 2's and 1's ?

d(n) = A236019(n) - a(n) = -1, -1, 1, 2, 3, 4, 4, 5, 6, 6, 6, 7, 7,... .

Nondecreasing numbers?

Examples

			Irregular triangle by consecutive odds and evens.
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,
etc.
Hence the unknown sequence b(n)=2, 2, 3, 4, 6, 8, 12, 15,... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A236019.

Programs

Mathematica

$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]A236019 = Table[a[n], {n, 0, 100}] ; A236444 = Complement[Range[A236019 // Last], A236019] (* Jean-François Alcover, Dec 17 2014, after Alois P. Heinz *)

Extensions

Offset corrected by Michel Marcus, Feb 12 2018