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A136015 Prime numbers n such that 2*n+1, n*(n+1)-1 and n*(n+1)+1 are also prime. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

3: prime

3+4=7 prime

3*4=12, 12-1=11 prime, 12+1=13 prime, 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 A042469

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

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)