A358149 First of four consecutive primes p,q,r,s such that (2*p+q)/5 and (r+2*s)/5 are prime.

11, 1151, 33071, 33637, 55331, 57637, 75997, 90821, 97007, 100151, 112237, 118219, 123581, 141629, 154459, 160553, 165961, 199247, 212777, 222823, 288361, 289511, 293677, 319993, 329471, 331697, 336101, 361799, 364537, 375371, 381467, 437279, 437693, 442571, 444461, 457837, 475751, 490877, 540781

Offset

1,1

Comments

Dickson's conjecture implies there are infinitely many terms where q = p+2, r = p+6 and s = p+8; the first two of these are 11 and 55331.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 33071 is a term because 33071, 33073, 33083, 33091 are four consecutive primes with (2*33071+33073)/5 = 19843 and (33083+2*33091)/5 = 19853 prime.

Maple

Res:= NULL: count:= 0:
q:= 2: r:= 3: s:= 5:
while count < 50 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  t:= (2*p+q)/5; u:= (r+2*s)/5;
  if (t::integer and u::integer and isprime(t) and isprime(u))
   then
    count:= count+1; Res:= Res, p;
  fi
od:
Res;

Mathematica

Select[Partition[Prime[Range[45000]], 4, 1], PrimeQ[(2*#[[1]] + #[[2]])/5] && PrimeQ[(#[[3]] + 2*#[[4]])/5] &][[;; , 1]] (* Amiram Eldar, Nov 01 2022 *)

Crossrefs

Cf. A358155.

Sequence in context: A045981 A090507 A177068 * A222827 A067105 A237695

Adjacent sequences: A358146 A358147 A358148 * A358150 A358151 A358152

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 01 2022

Status

approved