A007647 Numbers k such that k*10^k + 1 is prime. (Formerly M2783)

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

Offset

1,2

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

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

Table of n, a(n) for n=1..10.

Daniel Hermle, First Coordinated Generalized Cullen Prime Search.

Guenter Loeh, Generalized Cullen primes.

Example

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.

Prog

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

Crossrefs

Cf. A004023.

Sequence in context: A191998 A362341 A098980 * A247182 A363967 A318807

Adjacent sequences: A007644 A007645 A007646 * A007648 A007649 A007650

Keyword

hard,nonn

Author

N. J. A. Sloane

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

Status

approved