login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that 3*10^k + 1 is prime.
9

%I #44 Jan 28 2023 12:21:17

%S 1,3,7,10,28,36,67,81,147,483,643,1020,1900,2620,10453,27720,52824,

%T 105589,111988,618853,665829

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

%C Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019

%H S. W. Golomb, <a href="http://www.jstor.org/stable/2005337">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663.

%H S. W. Golomb, <a href="/A004119/a004119.pdf">Properties of the sequence 3.2^n+1</a>, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/30001.htm#prime">Prime numbers of the form 300...001</a>.

%H Sabin Tabirca and Kieran Reynolds, <a href="http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.

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

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

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

%o (PARI) is(k)=isprime(3*10^k+1) \\ _Charles R Greathouse IV_, Feb 17 2017

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

%K nonn,more

%O 1,2

%A _Robert G. Wilson v_, Aug 22 2000

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

%E a(15) from _Hugo Pfoertner_

%E a(16) & a(17) from _Robert G. Wilson v_, Jan 18 2005

%E a(18) from Roman Makarchuk, Dec 05 2008 confirmed as next term by _Ray Chandler_, Mar 02 2012

%E a(19) from Alexander Gramolin, Feb 24 2012 confirmed as next term by _Ray Chandler_, Mar 02 2012

%E a(20)-a(21) from Kamada data by _Robert Price_, Jan 26 2015