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URL: https://oeis.org/A116619

⇱ A116619 - OEIS

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A116619
a(n) = number of ways of representing 2*prime(n) as the unordered sum of two primes.
5
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
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) a(n)={my(c=0, k=2*prime(n)); forprime(p=2, prime(n), if(isprime(k-p), c++)); c} \\ Klaus Brockhaus, Dec 23 2006
(Haskell)
a116619 = (+ 1) . a071681 -- Reinhard Zumkeller, Mar 27 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 14 2006
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, Dec 23 2006
STATUS
approved