cp's OEIS Frontend

A152126 If f(x) = x^3+x^5+x^11+x^17+x^29+x^41+..., where the exponents are the smaller twin of twin prime pairs, consider {f(x)}^2 and write the exponents of that expansion down : x^6+2x^8+x^10+2x^12+.... The proposed sequence is that sequence of exponents.

%I A152126 #5 Jul 22 2025 06:15:52
%S A152126 6,8,10,14,16,20,22,28,32,34,40,44,46,52,58,62,64,70,74,76,82,88,100,
%T A152126 104,106,110,112,118,124,130,136,140,142,148,152,154,160,166,172,178,
%U A152126 182,184,190,194,196,200,202,208,214,220,226,230,232,238,242,244,250,256,262,268,272,274,280,284,286,292
%N A152126 If f(x) = x^3+x^5+x^11+x^17+x^29+x^41+..., where the exponents are the smaller twin of twin prime pairs, consider {f(x)}^2 and write the exponents of that expansion down : x^6+2x^8+x^10+2x^12+.... The proposed sequence is that sequence of exponents.
%C A152126 I would also like to tabulate the corresponding sequences for 3rd and higher powers of f(x) in separate sequences, maybe as far as 12th powers of f, assigning new numbers to each such sequence. For example, for the 3rd power, the sequence would begin {9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, etc. (the first "gap" appearing at 29). Each sequence would show no more than perhaps 500 (?) terms, or whatever number is needed to display a first gap.
%C A152126 Numbers of the form A001359(i)+A001359(j), including those of A108605 related to i=j. - _R. J. Mathar_, Nov 28 2008
%e A152126 I would like to show that some power of f(x) (as low a power as possible) contains no gaps. By this, I mean that the sequence of numbers in the m-th power of f should have the same parity as m and should start with 3m and that the sequence of odd (or even) numbers should have no gaps.
%K A152126 nonn
%O A152126 1,1
%A A152126 Paul Bruckman (pbruckman(AT)hotmail.com), Nov 25 2008
%E A152126 Corrected coefficient [x^10](f^2) in definition, inserted 34, extended. - _R. J. Mathar_, Nov 28 2008