A340494 Index where n first appears in A340488.

1, 3, 6, 8, 16, 18, 21, 23, 56, 58, 61, 63, 71, 73, 76, 78, 216, 218, 221, 223, 231, 233, 236, 238, 271, 273, 276, 278, 286, 288, 291, 293, 856, 858, 861, 863, 871, 873, 876, 878, 911, 913, 916, 918, 926, 928, 931, 933, 1071, 1073, 1076, 1078, 1086, 1088, 1091

Offset

0,2

Comments

The first differences appear to be some kind of ruler sequence separated by 2's.

indeed, the first differences look like n -> f(A001511(n)) with f = (2, 3, 8, 33, 138, 563, 2268, 9093, 36398, 145623, 582528, 2330153, 9320658, etc.). See A340495. - Rémy Sigrist, Jan 10 2021

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, PARI program for A340494

Formula

The generating function appears to be

1/(1-x ) + 2*x/(1-x)^2 + (1/(1-x))*Sum_{t>=1} x^(2^t)*(g(t+1)-g(t))/(1-x^(2^t)),

where g = {g(t): t >= 1} = 2,3,8,33,138,... has g.f. x*(2*x-1)*(2*x^2+5*x-2)/((1-x)^2*(1-4*x)). - Rémy Sigrist and N. J. A. Sloane, Jan 10 2021

Prog

(PARI) See Links section.

Crossrefs

Cf. A001511, A340488, A340495.

Sequence in context: A343272 A305595 A320687 * A039567 A032912 A123208

Adjacent sequences: A340491 A340492 A340493 * A340495 A340496 A340497

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2021

Extensions

More terms from Rémy Sigrist, Jan 10 2021

Status

approved