A116619 a(n) = number of ways of representing 2*prime(n) as the unordered sum of two primes.

1, 1, 2, 2, 3, 3, 4, 2, 4, 4, 3, 5, 5, 5, 5, 6, 6, 4, 6, 8, 6, 5, 6, 7, 7, 9, 7, 8, 7, 7, 9, 9, 11, 7, 11, 9, 9, 7, 11, 9, 10, 8, 10, 12, 11, 7, 11, 12, 12, 9, 13, 11, 11, 15, 14, 15, 14, 10, 11, 14, 13, 13, 15, 17, 12, 14, 14, 15, 19, 14, 19, 15, 15, 18, 15, 17, 15, 17, 16, 17, 17, 18, 17

Offset

1,3

Comments

2*prime(n) = A100484(n), the n-th even semiprime.

a(n) = A071681(n) + 1. - Reinhard Zumkeller, Mar 27 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A045917(A100484(n)).

Example

2*prime(23) = 166 can be represented in 6 ways as the unordered sum of two primes: 166 = 3+163 = 17+149 = 29+137 = 53+113 = 59+107 = 83+83, so a(23) = 6.
2*prime(54) = 502 can be represented in 15 ways as the unordered sum of two primes: 502 = 3+499 = 11+491 = 23+479 = 41+461 = 53+449 = 59+443 = 71+431 = 83+419 = 101+401 = 113+389 = 149+353 = 191+311 = 233+269 = 239+263 = 251+251, so a(54) = 15.

Prog

(PARI) {for(n=1, 83, c=0; k=2*prime(n); forprime(p=2, prime(n), if(isprime(k-p), c++)); print1(c, ", "))} - Klaus Brockhaus, Dec 23 2006
(Haskell)
a116619 = (+ 1) . a071681  -- Reinhard Zumkeller, Mar 27 2015

Crossrefs

Cf. A000040, A001358, A045917, A100484.

Cf. A071681, A010051.

Sequence in context: A356555 A339811 A015135 * A337776 A366611 A091220

Adjacent sequences: A116616 A116617 A116618 * A116620 A116621 A116622

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 14 2006

Extensions

Edited, corrected and extended by Klaus Brockhaus, Dec 23 2006

Status

approved