A296446 Numbers k such that 10^(2k)/2 + 10^k + 1 are prime.

1, 2, 3, 4, 7, 10, 56, 154, 170, 14728

Offset

1,2

Comments

Numbers of this form divide 10^(4k)+4.

a(10) > 5000. - Jon E. Schoenfield, Dec 16 2017

Links

Table of n, a(n) for n=1..10.

Example

61, 5101, 501001, 50010001, and 50000000010000000001 are prime, while 5000100001=13*1597*240841, 500001000001=2357*212134493, etc.

Mathematica

ParallelMap[If[PrimeQ[10^(2 #)/2 + 10^# + 1], #, Nothing] &, Range@ 4000] (* Robert G. Wilson v, Dec 13 2017 *)

Prog

(PARI) isok(k) = isprime(10^(2*k)/2+10^k+1); \\ Michel Marcus, Dec 13 2017

Crossrefs

See A296445 for 10^(2k)/2 - 10^k + 1.

Sequence in context: A094862 A104722 A270613 * A226387 A102282 A353178

Adjacent sequences: A296443 A296444 A296445 * A296447 A296448 A296449

Keyword

nonn,more

Author

Patrick A. Thomas, Dec 13 2017

Extensions

a(8)-a(9) from Michel Marcus, Dec 13 2017

a(10) from Michael S. Branicky, Aug 16 2024

Status

approved