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 A329446 Odd primes p such that p mod A001414((p+q)/2) and q mod A001414((p+q)/2) are prime, where q is the least prime > p. 1
 41, 47, 79, 103, 107, 151, 157, 167, 191, 229, 263, 283, 311, 313, 317, 337, 439, 521, 547, 557, 619, 631, 677, 691, 709, 727, 733, 761, 797, 809, 823, 853, 859, 863, 947, 953, 977, 991, 1051, 1091, 1103, 1151, 1153, 1213, 1229, 1289, 1301, 1327, 1429, 1447, 1471, 1487, 1493, 1511, 1607, 1627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If v is prime such that v-26, v-24, 6*v-1 and 6*v+1 are prime, then 6*v-1 is in the sequence. Dickson's conjecture implies there are infinitely many terms of this form. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(3)=79 is in the sequence because it is an odd prime, the next prime is 83, A001414((79+83)/2) = A001414(3^4) = 12, and 79 mod 12 = 7 and 83 mod 12 = 11 are both prime. MAPLE P:= select(isprime, [seq(i, i=3..2000, 2)]): Res:= NULL: for i from 1 to nops(P)-1 do m:= (P[i]+P[i+1])/2; L:= ifactors(m)[2]; M:= convert(map(convert, L, `*`), `+`); if isprime(P[i] mod M) and isprime(P[i+1] mod M) then Res:= Res, P[i] fi od: Res; PROG (Magma) [p:p in PrimesUpTo(1700)|IsPrime(p mod s) and IsPrime(NextPrime(p) mod s) where s is &+[j[1]*j[2]: j in Factorization((p+NextPrime(p)) div 2)] ]; // Marius A. Burtea, Nov 13 2019 CROSSREFS Cf. A001414. Sequence in context: A159023 A136294 A180547 * A243460 A186280 A039328 Adjacent sequences: A329443 A329444 A329445 * A329447 A329448 A329449 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Nov 13 2019 STATUS approved

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Last modified March 31 08:15 EDT 2023. Contains 361645 sequences. (Running on oeis4.)