A070689 Numbers k such that k+1 and k^2+1 are primes.

1, 2, 4, 6, 10, 16, 36, 40, 66, 126, 130, 150, 156, 180, 210, 240, 250, 256, 270, 280, 306, 396, 400, 420, 430, 466, 490, 556, 570, 576, 646, 690, 700, 750, 760, 826, 906, 910, 936, 946, 966, 1060, 1096, 1150, 1276, 1290, 1306, 1320, 1366, 1566, 1570

Offset: 1

Author

Robert G. Wilson v, May 13 2002

Keywords

• nonn

Comments

For any n > 1 in this sequence, (n+1)*(n^2+1) has the same nonzero digits as its prime factors in base n. - Ely Golden, Dec 12 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Crossrefs

Cf. A067720.

Programs

Mathematica

Select[ Range[2000], PrimeQ[ # + 1] && PrimeQ[ #^2 + 1] & ]
Select[Prime[Range[250]],PrimeQ[(#-1)^2+1]&]-1 (* Harvey P. Dale, Feb 10 2022 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim+1, if(isprime(1+(p-1)^2), listput(v,p-1))); Vec(v) \\ Charles R Greathouse IV, Dec 13 2016