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
Examples
k = 3 gives (3*10^3+1) = 3000+1 = 3001, which is prime.
Links
- 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.
Programs
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Mathematica
Do[ If[ PrimeQ[ 3*10^k + 1], Print[ k ]], {k, 0, 20000}] -
PARI
is(k)=isprime(3*10^k+1) \\ Charles R Greathouse IV, Feb 17 2017
Formula
a(n) = A101823(n) + 1.
Extensions
a(13)-a(14) from Julien Peter Benney (jpbenney(AT)ftml.net), Nov 23 2004
a(15) from Hugo Pfoertner, Jan 18 2005
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