A177960 Numbers of the form A001317(t), excluding those at places of the form t=m*(2^k-1), m>=0, k>=2.

3, 5, 17, 51, 257, 1285, 3855, 13107, 65537, 196611, 983055, 1114129, 5570645, 16711935, 50529027, 84215045, 858993459, 4294967297, 21474836485, 219043332147, 365072220245, 1103806595329, 3311419785987

Offset: 1

Author

Vladimir Shevelev, Dec 24 2010

Keywords

• nonn

Comments

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.

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,...

Crossrefs

Cf. A001317, A177882, A177897, A027907, A008287.

Formula

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.