A210339 Generalized Cullen primes: any primes that can be written in the form n*b^n + 1 with n+2 > b > 2.

19, 193, 52489, 114689, 9000000001, 259374246011, 38280596832649217, 59296646043258913, 408700964355468751, 2434970217729660813313, 13576803638250229989377, 21000000000000000000001, 3140085798164163223281069127, 4818833289797717549937328129

Offset

1,1

References

Harvey Dubner, Generalized Cullen numbers, J. Recreational Math. 21 (1989), pp. 190-194.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..92

Chris Caldwell, The Top 20 Generalized Cullen Primes

Chris Caldwell, The Prime Glossary, Cullen prime

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 57

G. L. Honaker, Jr. and Chris Caldwell, 15545...00001 (1008-digits)

G. L. Honaker, Jr. and Chris Caldwell, 36869...81251 (10002-digits)

PrimeGrid, Home Page

Wikipedia, Cullen number

Example

81*2^324 + 1 is a prime number and 81*2^324 + 1 = 81*16^81 + 1, so this number is in the sequence.

Mathematica

lst = {}; Do[p = n*b^n + 1; If[p < 10^200 && PrimeQ[p], AppendTo[lst, p]], {b, 3, 100}, {n, b - 1, 413}]; Sort@lst

Crossrefs

Cf. A050920, A005849, A006552, A007646.

Sequence in context: A120791 A048556 A141995 * A097445 A238697 A256639

Adjacent sequences: A210336 A210337 A210338 * A210340 A210341 A210342

Keyword

nonn

Author

Arkadiusz Wesolowski, Mar 20 2012

Status

approved