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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..2000
Crossrefs
Cf. A329151.
Programs
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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 *)
Comments