A296444 Numbers k such that 2*10^(2k) + 2*10^k + 1 are prime.

0, 2, 3, 6, 10, 276, 746, 1090, 1485, 6186, 8571, 15594

Offset

1,2

Comments

Numbers of this form divide 4*10^(4k)+1.

a(13) > 20000. - Michael S. Branicky, May 01 2025

Links

Table of n, a(n) for n=1..12.

Example

5, 20201, 2002001, 2000002000001, and 200000000020000000001 are prime, while 221=13*17, 200020001=569*351529, and 20000200001=17*29*1129*35933.

Mathematica

ParallelMap[ If[ PrimeQ[2*10^(2 #) + 2*10^# + 1], #, Nothing] &, Range@ 6500] (* Robert G. Wilson v, Dec 13 2017 *)

Prog

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

Crossrefs

See A296443 for 2*10^(2k)-2*10^k+1.

Cf. A297422, A309739.

Sequence in context: A371505 A186408 A062527 * A038752 A125714 A361593

Adjacent sequences: A296441 A296442 A296443 * A296445 A296446 A296447

Keyword

nonn,more

Author

Patrick A. Thomas, Dec 13 2017

Extensions

a(6)-a(7) from Michel Marcus, Dec 13 2017

a(8)-a(10) from Robert G. Wilson v, Dec 13 2017

a(1) = 0 inserted by Seiichi Manyama, Aug 15 2019

a(11) from Michael S. Branicky, Apr 16 2023

a(12) from Michael S. Branicky, Apr 30 2025

Status

approved