

A240712


Number of decompositions of 2n into an unordered sum of two terms of A240710.


5



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, 4, 7, 4, 4, 8, 4, 4, 9, 3, 5, 7, 3, 5, 8, 4, 5, 8, 5, 6, 10, 5, 6, 12, 4, 5, 10, 3, 6, 9, 5, 5, 8, 6, 7, 11, 6, 5, 12, 3, 7, 11, 5, 7, 10, 5, 5, 13, 8
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OFFSET

1,9


COMMENTS

a(n) differs from A171611 beginning at term a(264). To show the difference, the first 270 terms are listed.
Conjecture: a(n) > 0 for all n > 4.
This is a much stronger version of the Goldbach Conjecture.


LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000


EXAMPLE

For n < 264, please refer examples for A171611.
For n = 264, 2n=528. A240710 has terms {5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521} up to 528, where prime number 523 < 528 is not in the set, such that 528 = 5 + 523 is not counted in this sequence but is counted in A171611. So a(264) = A171611(264)1 = 251 = 24.


MATHEMATICA

a240710 = {5}; Table[s = 2*n; While[a240710[[1]] < s, p = a240710[[1]]; While[p = NextPrime[p]; ok = 0; a1 = p  12; a2 = p  6; a3 = p + 6; a4 = p + 12; If[a1 > 0, If[PrimeQ[a1], ok = 1]]; If[a2 > 0, If[PrimeQ[a2], ok = 1]]; If[PrimeQ[a3], ok = 1]; If[PrimeQ[a4], ok = 1]; ok == 0]; AppendTo[a240710, p]]; pos = 0; ct = 0; While[pos++; pos <= Length[a240710], p = a240710[[pos]]; If[p <= n, If[MemberQ[a240710, s  p], ct++]]]; ct, {n, 1, 270}]


CROSSREFS

Cf. A000040, A002375, A171611, A240710.
Sequence in context: A271319 A319178 A254041 * A171611 A239507 A216448
Adjacent sequences: A240709 A240710 A240711 * A240713 A240714 A240715


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Apr 10 2014


STATUS

approved



