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

Author

Arkadiusz Wesolowski, Mar 20 2012

Keywords

• nonn

Examples

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

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

Crossrefs

Cf. A050920, A005849, A006552, A007646.

Programs

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