A136015 Prime numbers p such that 2*p+1, p*(p + 1) - 1 and p*(p + 1) + 1 are also primes.

2, 3, 5, 41, 89, 131, 743, 761, 3449, 6173, 9059, 10781, 11549, 13553, 14939, 15569, 16301, 27809, 33479, 54773, 55439, 57149, 70901, 71849, 76091, 97523, 103391, 103643, 104369, 110543, 114269, 115499, 140111, 141539, 153509, 161033, 162251

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

3 is a term since it is a prime, 2 * 3 + 1 = 7 is a prime, 3 * (3 + 1) = 12, and (11, 13) are twin primes.

Maple

a:=proc(n) if isprime(n)=true and isprime(2*n+1)=true and isprime(n*(n+1)-1)= true and isprime(n*(n+1)+1)=true then n else end if end proc: seq(a(n), n=1.. 150000); # Emeric Deutsch, Apr 01 2008

Mathematica

a = ""; For[i = 1, i < 10^5, j = i + 1; s = i + j; m = i*j; p1 = m - 1; p2 = m + 1; If[PrimeQ[i] && PrimeQ[s] && PrimeQ[p1] && PrimeQ[p2], a = a <> ToString[i] <> ", "]; i++ ]; Print[a <> ".."]
Select[Prime[Range[100000]], PrimeQ[2# + 1] && PrimeQ[ #*(# + 1) - 1] && PrimeQ[ #*(# + 1) + 1] &] (* Stefan Steinerberger, Mar 24 2008 *)

Crossrefs

Sequence in context: A235681 A322748 A224781 * A106713 A106820 A362957

Adjacent sequences: A136012 A136013 A136014 * A136016 A136017 A136018

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 21 2008

Extensions

Edited with more terms by Stefan Steinerberger and Emeric Deutsch, Mar 24 2008

Status

approved