A332848 Primes p such that (3*p+q)/2, (p+3*q)/2, (3*q+r)/2 and (q+3*r)/2 are all prime, where q and r are the next primes after p.

809, 15331, 51071, 59183, 59447, 95747, 125737, 224069, 442733, 471677, 521869, 579757, 651517, 658873, 659453, 696989, 890887, 893449, 1035707, 1114193, 1236517, 1271807, 1299041, 1337593, 1435201, 1585513, 1590383, 1672271, 1707073, 1708363, 1817131, 1835003, 1963309, 1992527, 2078371, 2329597

Offset

1,1

Comments

The first of two consecutive primes that are both in A329151.

The first case where a(n+1) is the next prime after a(n), i.e. a(n) and the next two primes are all in A329151, is a(176)=35103361.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

a(3) = 51071 is in the sequence because p=51071, q=51109, r=51131 are consecutive primes such that (3*p+q)/2=102161, (p+3*q)/2=102199, (3*q+r)/2=102229, (q+3*r)/2=102251 are all prime.

Maple

q:= 3: r:= 5:
count:= 0: Res:= NULL:
while count < 100 do
  p:= q; q:= r; r:= nextprime(q);
  if isprime((3*p+q)/2) and isprime((p+3*q)/2) and isprime((3*q+r)/2)
  and isprime((q+3*r)/2) then
    count:= count+1; Res:= Res, p;
  fi
od:
Res;

Mathematica

Select[Partition[Prime[Range[175000]], 3, 1], AllTrue[{(3#[[1]]+#[[2]])/2, (#[[1]]+ 3#[[2]])/2, (3#[[2]]+#[[3]])/2, (#[[2]]+3#[[3]])/2}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Mar 19 2023 *)

Crossrefs

Cf. A329151.

Sequence in context: A252028 A031599 A265984 * A160561 A346716 A156404

Adjacent sequences: A332845 A332846 A332847 * A332849 A332850 A332851

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 26 2020

Status

approved