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

1,2

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?

Links

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

Example

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,... .

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]<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 *)

Crossrefs

Complement of A236019.

Sequence in context: A059552 A047516 A247425 * A286809 A352178 A244239

Adjacent sequences: A236441 A236442 A236443 * A236445 A236446 A236447

Keyword

nonn

Author

Paul Curtz, Jan 26 2014

Extensions

Offset corrected by Michel Marcus, Feb 12 2018

Status

approved