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 A253969 Primes p such that p + nextprime(p) is divisible by 6. 4
 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 59, 67, 71, 79, 89, 97, 101, 103, 107, 109, 113, 127, 137, 139, 149, 163, 179, 181, 191, 193, 197, 223, 227, 229, 239, 241, 269, 277, 281, 283, 293, 307, 311, 313, 317, 337, 347, 349, 359, 379, 389, 397, 401, 409, 419, 421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence provides all primes p such that p + nextprime(p) is divisible by 3 (see Crossrefs). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..10000 EXAMPLE p=19 is in this sequence because 19+23 = 42 is divisible by 6. MATHEMATICA Prime@Select[Range, Mod[Prime[#] + Prime[# + 1], 6]==0 &] Select[Partition[Prime[Range], 2, 1], Divisible[Total[#], 6]&][[All, 1]] (* Harvey P. Dale, Jan 20 2018 *) PROG (MAGMA) [p: p in PrimesUpTo(500) | (p+NextPrime(p)) mod 6 eq 0]; (PARI) forprime(p=1, 10^3, if(!((p+nextprime(p+1))%6), print1(p, ", "))) \\ Derek Orr, Jan 30 2015 CROSSREFS Cf. sum of prime p and next prime after p is divisible by k: A000040 (k=2, after the first term), this sequence (k=3, k=6), A098058(k=4, after the first term), A253970 (k=5; k=10 without 2), A179849 (k=7), A253972 (k=8), A253973 (k=9). Sequence in context: A171688 A239711 A217090 * A191056 A314296 A141639 Adjacent sequences:  A253966 A253967 A253968 * A253970 A253971 A253972 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 21 2015 STATUS approved

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Last modified August 7 11:56 EDT 2020. Contains 336276 sequences. (Running on oeis4.)