A137724 Prime numbers p such that p +- ((p-1)/6) are primes.

37, 181, 397, 757, 829, 1657, 2089, 2161, 2341, 3061, 5077, 6337, 7057, 7309, 7561, 8389, 9109, 9829, 10369, 10729, 13789, 17137, 21061, 21817, 21961, 23869, 24517, 24877, 25237, 26209, 28297, 29269, 31177, 31249, 32077, 32257, 33049, 33301, 35281, 38377, 39709, 41221, 42337, 44641, 47161

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

37+-6 = primes,
181+-30 = primes,
397+-(396/6) = primes.

Mathematica

w=6; s=""; For[i=1, i<10^3*2, p=Prime[i]; If[PrimeQ[p-((p-1)/w)]&&PrimeQ[p+((p-1)/w)], (*Print[p, ":", p-((p-1)/w), ", ", p+((p-1)/w)]; *)s=s<>ToString[p]<>", "]; i++ ]; Print[s]
Select[Prime[Range[50000]], PrimeQ[# + (# - 1) / 6]&& PrimeQ[# - (# - 1) / 6] &] (* Vincenzo Librandi, Jun 15 2013 °)
Select[Prime[Range[5000]], AllTrue[#+{(#-1)/6, -(#-1)/6}, PrimeQ]&] (* Harvey P. Dale, Jan 09 2024 *)

Prog

(Magma) [p: p in PrimesInInterval(5, 50000)| IsPrime((7*p-1) div 6 ) and IsPrime((5*p+1) div 6)]; // Vincenzo Librandi, Jun 15 2013

Crossrefs

Sequence in context: A195546 A142410 A164940 * A172080 A142181 A107196

Adjacent sequences: A137721 A137722 A137723 * A137725 A137726 A137727

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2008

Status

approved