|
Search: id:A136014
|
|
|
| A136014 |
|
Numbers n such that n*(n-1)-1 and n*(n+3)+1 are both prime. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
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 (deutsch(AT)duke.poly.edu), 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 (stefan.steinerberger(AT)gmail.com), Mar 24 2008
|
|
CROSSREFS
|
Adjacent sequences: A136011 A136012 A136013 this_sequence A136015 A136016 A136017
Sequence in context: A047251 A092999 A136495 this_sequence A112930 A003159 A141259
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2008
|
|
EXTENSIONS
|
Edited with more terms by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 24 2008
|
|
|
Search completed in 0.002 seconds
|
