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

1,2

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A067720.

Sequence in context: A164142 A048833 A204656 * A339312 A091611 A107742

Adjacent sequences: A070686 A070687 A070688 * A070690 A070691 A070692

Keyword

nonn

Author

Robert G. Wilson v, May 13 2002

Status

approved