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 A240708 Number of decompositions of 2n into an unordered sum of two terms of A240699. 6
 0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, 4, 3, 4, 5, 4, 3, 5, 3, 4, 6, 3, 5, 6, 2, 5, 6, 5, 5, 7, 4, 5, 8, 5, 4, 9, 4, 5, 7, 3, 6, 8, 5, 6, 8, 6, 7, 10, 6, 6, 12, 4, 5, 10, 3, 7, 9, 6, 5, 8, 7, 8, 11, 6, 5, 12, 4, 8, 11, 5, 8, 10, 5, 6, 13, 9, 6, 11, 7, 7, 14, 6, 8, 13, 5, 8, 11, 7, 9, 13, 8, 9, 14, 7, 7, 19, 6, 7, 12, 6, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The first different term of this sequence to A002375 is a(107). Conjecture: for n >= 3, this sequence is always positive. This is a stronger version of the Goldbach Conjecture. LINKS Lei Zhou, Table of n, a(n) for n = 1..10000 EXAMPLE For n <= 106, refer to examples in A002375. For n = 107, 2n=214. A240699 up to 214 gives {3, 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}.  We have 214 = 17+197 = 23+191 = 41+173 = 47+167 = 83+131 = 101+113 = 107+107. Seven instances found. So a(107)=7. Where as for A002375, there is one more instance as 3+211, however 211 is not a term in A240699. MATHEMATICA a240699 = {3}; Table[s = 2*n; While[a240699[[-1]] < s, p = a240699[[-1]]; While[p = NextPrime[p]; ((NextPrime[p] - p) > 6) && (6 < (p - NextPrime[p, -1]))]; AppendTo[a240699, p]]; pos = 0; ct = 0; While[pos++; pos <= Length[a240699], p = a240699[[pos]]; If[p <= n, If[MemberQ[a240699, s - p], ct++]]]; ct, {n, 1, 110}] CROSSREFS Cf. A000040, A002375, A045917, A240699. Sequence in context: A254610 A002375 A045917 * A235645 A325357 A294107 Adjacent sequences:  A240705 A240706 A240707 * A240709 A240710 A240711 KEYWORD nonn,easy AUTHOR Lei Zhou, Apr 10 2014 STATUS approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)