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%I #22 Jul 18 2021 21:00:46
%S 3,5,17,51,257,1285,3855,13107,65537,196611,983055,1114129,5570645,
%T 16711935,50529027,84215045,858993459,4294967297,21474836485,
%U 219043332147,365072220245,1103806595329,3311419785987
%N Numbers of the form A001317(t), excluding those at places of the form t=m*(2^k-1), m>=0, k>=2.
%C m-nomial (m>=2) coefficients are coefficients of the polynomial (1+x+...+x^(m-1))^n (n>=0), see A007318 (m=2), A027907 (m=3), A008287 (m=4), A035343 (m=5) etc. For k>=1, consider the triangle of 2^k-nomial coefficients, each entry reduced mod 2, and convert each row of the reduced triangle to a single number by interpreting the sequence of bits as binary representation of a number. This defines sequences A001317 (k=1), A177882 (k=2), A177897 (k=3), etc. The current sequence lists terms of A001317 which are not derived from any of the sequences for k >=2, not from 4-nomial, not from 8-nomial, not from 16-nomial etc.
%C Conjecture: If for every m>=2, to consider triangle of m-nomial coefficients mod 2 converted to decimal, then the sequence lists terms of A001317 which are not in the union of other sequences for m=3 (A038184), 4 (A177882), 5, 6,...
%F Denote by B(n) the number of terms of the sequence among the first n terms of A001317. Then lim_{n->infinity} B(n)/ = Product_{prime p>=2} (1 - 1/(2^p-1)) = A184085.
%Y Cf. A001317, A177882, A177897, A027907, A008287.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Dec 24 2010
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