A136014 Numbers n such that n*(n-1)-1 and n*(n+3)+1 are both prime.

3, 4, 5, 7, 9, 10, 12, 14, 20, 25, 27, 29, 40, 45, 47, 49, 54, 55, 65, 67, 69, 84, 95, 102, 139, 154, 159, 170, 175, 185, 187, 192, 194, 219, 232, 245, 247, 264, 289, 295, 297, 302, 304, 350, 359, 379, 392, 394, 419, 432, 449, 454, 462, 472, 474, 495, 500

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Example

3,s=3+4=7,t=3*4=12,t-s=12-7=5, prime, t+s=12+5=17, prime
4,s=4+5=9,t=4*5=20,t-s=20-9=11, prime,t+s=20+9=29, prime

Maple

a:=proc(n) local s, t: s:= 2*n+1: t:= n*(n+1): if isprime(t-s)=true and isprime(t+s)=true then n else end if end proc: seq(a(n), n=1..400); # Emeric Deutsch, Mar 31 2008

Mathematica

a = ""; For[i = 1, i < 10^2, j = i + 1; s = i + j; m = i*j; p1 = m - s; p2 = m + s; If[PrimeQ[p1] && PrimeQ[p2], a = a <> ToString[i] <> ", "]; i++ ]; Print[a <> ".."]
Select[Range[500], PrimeQ[ #*(# - 1) - 1] && PrimeQ[ #*(# + 3) + 1] &] (* Stefan Steinerberger, Mar 24 2008 *)

Crossrefs

Sequence in context: A285970 A189665 A156246 * A112930 A224985 A282808

Adjacent sequences: A136011 A136012 A136013 * A136015 A136016 A136017

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