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 A343974 Even numbers k such that the two sets of primes in the Goldbach representation of k and k+2 as the sum of two odd primes do not intersect. 0
 38, 68, 80, 98, 122, 128, 146, 158, 164, 188, 206, 212, 218, 224, 248, 278, 290, 302, 308, 326, 332, 338, 344, 368, 374, 380, 398, 410, 416, 428, 440, 458, 476, 488, 500, 518, 530, 536, 542, 548, 554, 578, 584, 608, 614, 626, 632, 638, 668, 674, 692, 698, 710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS k is in the sequence iff the Goldbach representation of k as the sum of two odd primes does not contain any prime that is the lesser of a twin prime (A001359). Conjecture: a(n) is congruent to 2 mod 6 with a(n)-3 not prime. LINKS Table of n, a(n) for n=1..53. Mahdi Meisami and Carlos Rivera, Puzzle 1040. Pair of consecutive even integers such that ..., The Prime Puzzles & Problems Connection. FORMULA a(n) = 6*A046953(n) + 2 (conjectured). - Hugo Pfoertner, Jun 09 2021 EXAMPLE The Goldbach representations of 80 and 82 as the sum of two odd primes are: {{73, 7}, {67, 13}, {61, 19}, {43, 37}} and {{79, 3}, {71, 11}, {59, 23}, {53, 29}, {41, 41}}. The two sets {7, 13, 19, 37, 43, 61, 67, 73} and {3, 11, 23, 29, 41, 53, 59, 71, 79} do not intersect, so 80 is a term of the sequence. MATHEMATICA Select[Range[6, 1000, 2], !IntersectingQ@@(Flatten@Select[IntegerPartitions[#, 2], And@@PrimeQ[#]&]&/@{#, #+2})&] CROSSREFS Cf. A001359, A046953. Sequence in context: A216140 A177044 A321997 * A335483 A071885 A032506 Adjacent sequences: A343971 A343972 A343973 * A343975 A343976 A343977 KEYWORD nonn AUTHOR Giorgos Kalogeropoulos, Jun 07 2021 STATUS approved

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Last modified September 11 01:27 EDT 2024. Contains 375813 sequences. (Running on oeis4.)