

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


0



6, 8, 10, 14, 16, 20, 22, 28, 32, 34, 40, 44, 46, 52, 58, 62, 64, 70, 74, 76, 82, 88, 100, 104, 106, 110, 112, 118, 124, 130, 136, 140, 142, 148, 152, 154, 160, 166, 172, 178, 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
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OFFSET

1,1


COMMENTS

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.
Numbers of the form A001359(i)+A001359(j), including those of A108605 related to i=j.  R. J. Mathar, Nov 28 2008


LINKS

Table of n, a(n) for n=1..66.


EXAMPLE

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 mth 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.


CROSSREFS

Sequence in context: A294729 A242270 A298252 * A315853 A065858 A243537
Adjacent sequences: A152123 A152124 A152125 * A152127 A152128 A152129


KEYWORD

nonn


AUTHOR

Paul Bruckman (pbruckman(AT)hotmail.com), Nov 25 2008


EXTENSIONS

Corrected coefficient [x^10](f^2) in definition, inserted 34, extended.  R. J. Mathar, Nov 28 2008


STATUS

approved



