

A254690


Number of decompositions of 2n into a sum of two primes p1 < p2 such that p2p1 is between a pair of sexy primes.


1



0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 1, 3, 3, 2, 3, 5, 4, 2, 5, 2, 3, 5, 2, 4, 6, 2, 5, 6, 3, 4, 6, 4, 3, 7, 2, 3, 8, 3, 4, 6, 2, 5, 7, 3, 3, 7, 5, 5, 8, 4, 3, 9, 2, 4, 8, 2, 5, 7, 2, 2, 4, 6, 5, 7, 4, 2, 10, 2, 4, 7, 1, 6, 7, 1, 4, 10, 7, 3, 8
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OFFSET

1,8


COMMENTS

"A pair of sexy primes" is defined as two primes p_a < p_b such that p_b = p_a + 6, with p_a from A023201. See the Weisstein link.
The restriction is therefore p_a < p2  p1 < p_a + 6 for p_a from A023201.
Conjecture: when n>=7, a(n)>0.
The products of sexy prime pairs are listed in A111192.


LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, 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].
Lei Zhou, Plot of a(n) for n <= 20000.


EXAMPLE

n=7, 2n=14=3+11. 113=8, 5<8<11 where {5, 11} is a pair of sexy primes. So a(7)=1.
n=8, 2n=16=3+13=5+11. 133=10, 5<10<11; 115=6, 5<6<11, where {5, 11} is a pair of sexy primes: two cases found, so a(8)=2.
n=17, 2n=34=3+31=5+29=11+23. 313=28, 23<28<29; 295=24, 23<24<29; 2311=12, 7<12<13; where {23,29} and {7,13} are sexy prime pairs: three cases found, so a(17)=3.


MATHEMATICA

Table[e = 2 n; ct = 0; p1 = 1; While[p1 = NextPrime[p1]; p1 < n, p2 = e  p1; If[PrimeQ[p2], c = p2  p1; If[c >= 6, found = 0; Do[If[PrimeQ[c  i] && PrimeQ[c + 6  i], found = 1], {i, 1, 5, 2}]; If[found == 1, ct++]]]]; ct, {n, 1, 100}]


CROSSREFS

Cf. A023201, A045917, A111192.
Sequence in context: A331971 A030547 A339932 * A156642 A155124 A138033
Adjacent sequences: A254687 A254688 A254689 * A254691 A254692 A254693


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Feb 05 2015


EXTENSIONS

Edited by Wolfdieter Lang, Feb 20 2015


STATUS

approved



