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 A278693 Numbers n such that prime(n) + prime(n+1) is divisible by 2n + 1. 0
 4, 181, 6458, 6460, 40083, 40121, 10553502, 69709942, 3140421718, 3140421737, 3140421740, 3140421768, 3140421805, 3140421845 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The pairs of consecutive prime numbers corresponding to the terms of this sequence are 7,11; 1087,1091; 64579,64591; 64601,64609; 481001,481003; 481447,481469; 189963043,189963047; ... The corresponding integers (prime(k) + prime(k+1))/(2*k+1) are 2, 6, 10, 10, 12, 12, 18, ... LINKS EXAMPLE a(1) = 4 since prime(4) + prime(5) = 7 + 11 = 18 is divisible by 2*4 + 1 = 9. a(2) = 181 since prime(181) + prime(182) = 1087 + 1091 = 2178 is divisible by 2*181 + 1 = 363. a(3) = 6458 since prime(6458) + prime(6459) = 64579 + 64591 = 129170 is divisible by 2*6458 + 1 = 12917. a(4) = 6460 since prime(6460) + prime(6461) = 64601 + 64609 = 129210 is divisible by 2*6460 + 1 = 12921. a(5) = 40083 since prime(40083) + prime(40084) = 481001 + 481003 = 962004 is divisible by 2*40083 + 1 = 80167. a(6) = 40121 since prime(40121) + prime(40122) = 481447 + 481469 = 962916 is divisible by 2*40121 + 1 = 80243. a(7) = 10553502 since prime(10553502) + prime(10553503) = 189963043 + 189963047 = 379926090 is divisible by 2*10553502 + 1 = 21107005. a(8) = 69709942 since prime(69709942) + prime(69709943) = 1394198837 + 1394198863 = 2788397700 is divisible by 2*69709942 + 1 = 139419885. a(9) = 3140421718 since prime(3140421718) + prime(3140421719) = 75370121237 + 75370121251 = 150740242488 is divisible by 2*3140421718 + 1 = 6280843437. a(10) = 3140421737 since prime(3140421737) + prime(3140421738) = 75370121689 + 75370121711 = 150740243400 is divisible by 2*3140421737 + 1 = 6280843475. a(11) = 3140421740 since prime(3140421740) + prime(3140421741) = 75370121767 + 75370121777 = 150740243544 is divisible by 2*3140421740 + 1 = 6280843481. a(12) = 3140421768 since prime(3140421768) + prime(3140421769) = 75370122439 + 75370122449 = 150740244888 is divisible by 2*3140421768 + 1 = 6280843537. a(13) = 3140421805 since prime(3140421805) + prime(3140421806) = 75370123327 + 75370123337 = 150740246664 is divisible by 2*3140421805 + 1 = 6280843611. a(14) = 3140421845 since prime(3140421845) + prime(3140421846) = 75370124273 + 75370124311 = 150740248584 is divisible by 2*3140421845 + 1 = 6280843691. PROG (PARI) isok(k) = denominator((prime(k)+prime(k+1))/(2*k+1)) == 1; \\ Michel Marcus, Nov 26 2016 (PARI) n=0; p=2; forprime(q=3, 1e9, n++; if((p+q)%(2*n+1)==0, print1(n", ")); p=q) \\ Charles R Greathouse IV, Nov 28 2016 CROSSREFS Cf. A000040, A001043. Sequence in context: A269195 A269102 A240282 * A172018 A295285 A322915 Adjacent sequences:  A278690 A278691 A278692 * A278694 A278695 A278696 KEYWORD nonn,more AUTHOR Emre APARI, Nov 26 2016 EXTENSIONS a(8)-a(14) from Charles R Greathouse IV, Nov 28 2016 STATUS approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)