1,1

A083097(n) = A083095(n) = A083096(n)/6 = A083094(n)/4, where A083096(n) are the Numbers n such that 3 divides sum(k=1,n, C(2k,k) ) = A066796(n). All a(n) are of the form (9m + 5) and belong to A017221[m] with m = {0,1,4,6,13,15,18,19,40,42,...}. Corresponding numbers n such that a(n) = A083097(n) are {2,4,8,14,16,22,26,28,32,38,42,44,50,...} = A074202(n+1), where A074202(n) are the numbers n such that the number of 1's in the binary representation of n divides 2^n-1. Note that A074202(n) = 2*A000069(n-2) = 4n - 7 + (-1)^A000120(n-2) for n>1, where A000069(n) are Odious numbers: odd number of 1's in binary expansion; and A000120(n) is 1's-counting sequence: number of 1's in binary expansion of n.

a(n) = A083097[ A074202(n+1) ]. a(n) = A083097[ 2 * A000069(n-1) ]. a(n) = A083097[ 4n - 3 + (-1)^A000120(n-1) ].

A083097(n) begins {0,2,5,6,14,15,18,20,41,42,45,47,54,56,59,60,122,123,...}.

So a(1) = 5 because 5 = A083097[2] = A083097[2+1] - 1.

a(2) = 14 because 14 = A083097[4] = A083097[4+1] - 1.

Cf. A083097, A066796, A083096, A083095, A083094, A017221, A010060, A074202, A000069, A000120.

Sequence in context: A119996 A027089 A023871 this_sequence A032249 A129937 A147978

Adjacent sequences: A122482 A122483 A122484 this_sequence A122486 A122487 A122488

more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 15 2006

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 17 2008