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A136014 Numbers n such that n*(n-1)-1 and n*(n+3)+1 are both prime. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited with more terms by Stefan Steinerberger and Emeric Deutsch, Mar 24 2008
STATUS
approved

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Last modified June 25 11:18 EDT 2024. Contains 373701 sequences. (Running on oeis4.)