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.

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

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