[seqfan] Re: polynomial-to-product transform
Neil Fernandez
primeness at borve.org
Sun Nov 9 22:44:56 CET 2008
Two things:
1) a product-to-polynomial transform on the primes gives:
(1+2x)(1+3x^2)(1+5x^3)(1+7x^4)(1+11x^5)...= 1+2x+3x^2+11x^3+...
and the sequence beginning
{2,3,11,17,40,86,153,283,547,1069,1737,3238,5340,9574,17251,27897,45845,
78601,126725,207153,...}
Does a(n)/a(n-1) tend to a constant?
2) the polynomial-to-product transform of the positive integers
1,2,3,... gives:
1+1x+2x^2+3x^3+4x^4... = (1+b(1)x)(1+b(2)x^2)... where {b(1),b(2),...}
is the sequence:
{1,2,1,3,0,-2,0,9,0,-6,0,4,0,-18,0,93,0,-54,0,72,0,-186,0,232}
Neil
--
Neil Fernandez
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