login
Index where n first appears in A340488.
5

%I #28 Jan 10 2021 14:42:58

%S 1,3,6,8,16,18,21,23,56,58,61,63,71,73,76,78,216,218,221,223,231,233,

%T 236,238,271,273,276,278,286,288,291,293,856,858,861,863,871,873,876,

%U 878,911,913,916,918,926,928,931,933,1071,1073,1076,1078,1086,1088,1091

%N Index where n first appears in A340488.

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

%C 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

%H Rémy Sigrist, <a href="/A340494/b340494.txt">Table of n, a(n) for n = 0..8191</a>

%H Rémy Sigrist, <a href="/A340494/a340494.gp.txt">PARI program for A340494</a>

%F The generating function appears to be

%F 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)),

%F 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

%o (PARI) See Links section.

%Y Cf. A001511, A340488, A340495.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 10 2021

%E More terms from _Rémy Sigrist_, Jan 10 2021