|
%I #13 Apr 03 2023 10:36:13
%S 19,193,52489,114689,9000000001,259374246011,38280596832649217,
%T 59296646043258913,408700964355468751,2434970217729660813313,
%U 13576803638250229989377,21000000000000000000001,3140085798164163223281069127,4818833289797717549937328129
%N Generalized Cullen primes: any primes that can be written in the form n*b^n + 1 with n+2 > b > 2.
%D Harvey Dubner, Generalized Cullen numbers, J. Recreational Math. 21 (1989), pp. 190-194.
%H Arkadiusz Wesolowski, <a href="/A210339/b210339.txt">Table of n, a(n) for n = 1..92</a>
%H Chris Caldwell, <a href="https://t5k.org/top20/page.php?id=42">The Top 20 Generalized Cullen Primes</a>
%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/Cullens.html">Cullen prime</a>
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/21842.html">Prime Curios! 57</a>
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/19503.html">15545...00001 (1008-digits)</a>
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/20075.html">36869...81251 (10002-digits)</a>
%H PrimeGrid, <a href="http://www.primegrid.com">Home Page</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cullen_number">Cullen number</a>
%e 81*2^324 + 1 is a prime number and 81*2^324 + 1 = 81*16^81 + 1, so this number is in the sequence.
%t 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
%Y Cf. A050920, A005849, A006552, A007646.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Mar 20 2012
| 