A137705 Prime numbers p such that p +- ((p-1)/4) are primes.

1489, 2377, 2689, 2857, 3361, 3889, 4969, 5569, 6481, 6577, 7537, 8089, 10009, 11257, 14281, 14449, 14929, 15601, 16057, 17569, 18121, 19249, 21817, 22441, 24169, 24697, 25057, 26881, 27481, 30937, 31081, 33289, 33409, 33529, 33961, 36097, 39841

Offset

1,1

Links

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

Example

1489+1488/4 = 1861 and 1489-1488/4 = 1117, which are primes;
2377+2376/4 = 2971 and 2377-2376/4 = 1783, which are primes.

Mathematica

w=4; 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) / 4]&& PrimeQ[# - (# - 1) / 4] &] (* Vincenzo Librandi, Jun 15 2013 *)

Prog

(Magma) [p: p in PrimesInInterval(5, 40000)| IsPrime((5*p-1) div 4 ) and IsPrime((3*p+1) div 4)]; // Vincenzo Librandi, Jun 15 2013

Crossrefs

Sequence in context: A237244 A028515 A288727 * A367769 A171617 A067841

Adjacent sequences: A137702 A137703 A137704 * A137706 A137707 A137708

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2008

Status

approved