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A137705 Prime numbers p such that p +- ((p-1)/4) are primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A171617 A067841 A237968

Adjacent sequences:  A137702 A137703 A137704 * A137706 A137707 A137708

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 27 2008

STATUS

approved

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Last modified May 31 12:48 EDT 2020. Contains 334748 sequences. (Running on oeis4.)