A007647 Numbers k such that k*10^k + 1 is prime.

1, 3, 9, 21, 363, 2161, 4839, 49521, 105994, 207777

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn

Comments

These are generalized Cullen numbers in base 10. - Julien Peter Benney (jpbenney(AT)ftml.net), Oct 24 2004

No others less than 270026. - Ray Chandler, Apr 10 2016

Examples

			For k = 3 we get (3*10^3)+1 = (3*1000)+1 = 3000 + 1 = 3001, which is prime.
For k = 9 we get 9*10^9+1 = 9*1000000000+1 = 9000000000+1 = 9000000001, which is prime.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 363, p. 84, Ellipses, Paris 2008.
• H. Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190-191.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Daniel Hermle, First Coordinated Generalized Cullen Prime Search.
• Guenter Loeh, Generalized Cullen primes.

Crossrefs

Cf. A004023.

Programs

PARI

is(n)=ispseudoprime(n*10^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Julien Peter Benney (jpbenney(AT)ftml.net), Jun 11 2005

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007

a(10) from Loeh link by Ray Chandler, Apr 10 2016