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A088627 Let 2n = r*s. Then a(n) = number of primes of the form r+s (r= 1 and s = 2n contributes 1 to the count if 2n+1 is prime). +0
2
1, 1, 2, 0, 2, 2, 0, 1, 2, 0, 2, 1, 0, 2, 4, 0, 1, 2, 0, 2, 4, 0, 1, 1, 0, 2, 1, 0, 2, 4, 0, 0, 2, 0, 4, 2, 0, 1, 4, 0, 2, 2, 0, 2, 3, 0, 0, 1, 0, 2, 4, 0, 1, 2, 0, 2, 2, 0, 1, 3, 0, 0, 2, 0, 4, 3, 0, 1, 3, 0, 1, 0, 0, 2, 3, 0, 2, 2, 0, 1, 2, 0, 1, 3, 0, 2, 2, 0, 1, 3, 0, 1, 1, 0, 4, 2, 0, 2, 4, 0, 1, 2, 0, 1, 8 (list; graph; listen)
OFFSET

1,3

COMMENT

Only even numbers yield primes hence odd numbers are not considered.

There is an upper bound: if n has only k different prime divisors > 2, then a(n) <= 2^k. - Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de), Jan 05 2004

LINKS

M. Engelhardt, Number of Primes arising as Sum of a Factorization.

EXAMPLE

a(9) = 2 18 = 1*18, 1+18= 19 and 18 = 2*9, 2+9 = 11, two primes arise.

CROSSREFS

Cf. A091350.

Sequence in context: A028928 A091379 A106277 this_sequence A024713 A123530 A123063

Adjacent sequences: A088624 A088625 A088626 this_sequence A088628 A088629 A088630

KEYWORD

nonn

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 19 2003

EXTENSIONS

More terms from Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de), Jan 05 2004

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 15 2005

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.


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