login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A254041 Number of decompositions of 2n into an unordered sum of two sexy primes. 1
0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 2, 3, 1, 3, 4, 2, 2, 4, 2, 3, 5, 3, 3, 5, 2, 4, 6, 2, 4, 6, 2, 4, 6, 4, 3, 6, 4, 3, 7, 4, 3, 8, 3, 4, 7, 3, 4, 7, 4, 5, 7, 5, 5, 9, 5, 5, 12, 4, 4, 10, 3, 5, 7, 4, 5, 6, 5, 6, 8, 4, 5, 9, 2, 5, 8, 3, 5, 8, 4, 4, 9, 6, 4, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
"Sexy primes" are listed in A136207.
It is conjectured that a(n) > 0 for n > 4.
LINKS
Eric Weisstein's World of Math, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021]
Wikipedia, Sexy Primes
Lei Zhou, Plot of a(n) up to n=1000000.
EXAMPLE
When n = 79, 2n = 158 = 7 + 151 = 19 + 139 = 31 + 127 = 61 + 97 = 79 + 79 has five "two prime decompositions". Among the involved prime numbers 7, 19, 31, 61, 79, 97, 127, 139, 151, prime 127 and 139 are not sexy primes. So only three decompositions, 158 = 7 + 151 = 61 + 97 = 79 + 79 satisfy the definition of this sequence. Thus a(79) = 3.
MATHEMATICA
Table[e = 2 n; ct = 0; p = 2; While[p = NextPrime[p]; p <= n, q = e - p; If[PrimeQ[q], If[(((p > 6) && PrimeQ[p - 6]) || PrimeQ[p + 6]) && (((q > 6) && PrimeQ[q - 6]) || PrimeQ[q + 6]), ct++]]]; ct, {n, 87}]
CROSSREFS
Sequence in context: A271319 A367404 A319178 * A240712 A171611 A239507
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, Jan 23 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)