A239115 Numbers n such that (n-1)*n^2-1 and n^2-(n-1) are both prime.
2, 3, 4, 6, 7, 9, 13, 18, 21, 22, 58, 67, 79, 90, 100, 106, 111, 118, 120, 144, 162, 174, 195, 204, 246, 273, 279, 345, 393, 403, 406, 435, 436, 526, 541, 567, 613, 625, 636, 702, 721, 729, 736, 744, 762, 763, 865, 898, 961, 970, 993, 1059, 1099, 1117, 1131
Offset: 1
Keywords
Examples
13 is in this sequence because (13-1)*13^2-1 = 2027 and 13^2-(13-1) = 157 are both prime.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..10000
Programs
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Magma
k:=1; for n in [1..1000] do if IsPrime(k*(n-1)*n^2-1) and IsPrime(k*n^2-n+1) then n; end if; end for; // Juri-Stepan Gerasimov, Mar 18 2014 -
Mathematica
Select[Range[1000], PrimeQ[#^3 - #^2 - 1] && PrimeQ[#^2 - # + 1] &] (* Giovanni Resta, Mar 10 2014 *) Select[Range[1200],PrimeOmega[#^5-2#^4+2#^3-2#^2+#-1]==2&] (* Harvey P. Dale, Sep 24 2014 *)
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PARI
isok(n) = isprime(n^3-n^2-1) && isprime(n^2-n+1); \\ Michel Marcus, Mar 10 2014
Extensions
More terms from Giovanni Resta, Mar 10 2014
Comments