A056807 Numbers k such that 3*10^k + 1 is prime.

1, 3, 7, 10, 28, 36, 67, 81, 147, 483, 643, 1020, 1900, 2620, 10453, 27720, 52824, 105589, 111988, 618853, 665829

Offset

1,2

Comments

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Links

Table of n, a(n) for n=1..21.

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.

S. W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]

Makoto Kamada, Prime numbers of the form 300...001.

Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Formula

a(n) = A101823(n) + 1.

Example

k = 3 gives (3*10^3+1) = 3000+1 = 3001, which is prime.

Mathematica

Do[ If[ PrimeQ[ 3*10^k + 1], Print[ k ]], {k, 0, 20000}]

Prog

(PARI) is(k)=isprime(3*10^k+1) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A056797, A062339, A101823, A199683, A259866.

Sequence in context: A041525 A251862 A363651 * A146927 A193650 A041783

Adjacent sequences: A056804 A056805 A056806 * A056808 A056809 A056810

Keyword

nonn,more

Author

Robert G. Wilson v, Aug 22 2000

Extensions

a(13) & a(14) from Julien Peter Benney (jpbenney(AT)ftml.net), Nov 23 2004

a(15) from Hugo Pfoertner

a(16) & a(17) from Robert G. Wilson v, Jan 18 2005

a(18) from Roman Makarchuk, Dec 05 2008 confirmed as next term by Ray Chandler, Mar 02 2012

a(19) from Alexander Gramolin, Feb 24 2012 confirmed as next term by Ray Chandler, Mar 02 2012

a(20)-a(21) from Kamada data by Robert Price, Jan 26 2015

Status

approved