This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005849 M5401 #72 Feb 16 2025 08:32:29 %S A005849 1,141,4713,5795,6611,18496,32292,32469,59656,90825,262419,361275, %T A005849 481899,1354828,6328548,6679881 %N A005849 Indices of prime Cullen numbers: numbers k such that k*2^k + 1 is prime. %C A005849 From _Amiram Eldar_, Jun 05 2021: (Start) %C A005849 The terms were found by: %C A005849 a(1) - Cullen (1905). He found that there are no other terms up to 100 with the possible exception of 53. Cunningham (1906) showed that the 53rd Cullen number is composite and that the only possible term up to 200 is 141. %C A005849 a(2) - Robinson (1958). %C A005849 a(3)-a(6) - Keller (1995). %C A005849 a(7)-a(8) - Masakatu Morii (1997). %C A005849 a(9)-a(10) - Jeffrey Young (1997). %C A005849 a(11)-a(12) - Darren Smith (1998). %C A005849 a(13) - Masakatu Morii (1998). %C A005849 a(14) - Mark Rodenkirch (2005). %C A005849 a(15) - Dennis R. Gesker (2009). %C A005849 a(16) - Magnus Bergman (2009). (End) %D A005849 A. J. Cunningham, Solution of question 15897, Math. Quest. Educ. Times, Vol. 10 (1906), pp. 44-47. %D A005849 Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 141, p. 48, Ellipses, Paris 2008. %D A005849 Harvey Dubner, Generalized Cullen numbers, J. Rec. Math., Vol. 21, No. 3 (1989), pp. 190-191. %D A005849 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20. %D A005849 Paulo Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 283. %D A005849 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005849 Ray Ballinger, <a href="http://web.archive.org/web/20161028015144/http://www.prothsearch.net/cullen.html">Cullen Primes: Definition and Status</a>. %H A005849 Chris K. Caldwell, <a href="https://t5k.org/top20/page.php?id=6">The Top Twenty: Cullen Primes</a>. %H A005849 Allan Cunningham and H. J. Woodall, <a href="https://archive.org/details/messengerofmathe47cambuoft/page/22/mode/2up">Factorisation of Q = (2^q -/+ q) and (q*2^q -\+ 1)</a>, The Messenger of Mathematics, Vol. 47 (1917-18), pp. 1-38. See p. 22. %H A005849 Harvey Dubner, <a href="/A005849/a005849.pdf">Generalized Cullen numbers</a>, J. Rec. Math., Vol. 21, No. 3 (1989), pp. 190-191. (Annotated scanned copy) %H A005849 Wilfrid Keller, <a href="https://doi.org/10.1090/S0025-5718-1995-1308456-3">New Cullen primes</a>, Mathematics of Computation, Vol. 64, No. 212 (1995), pp. 1733-1741. %H A005849 Rudolf Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/">The Top Ten: a Catalogue of Primal Configurations</a>. %H A005849 PrimeGrid, <a href="http://www.primegrid.com/primes/primes.php?project=CUL">PrimeGrid Primes: Subproject: (CUL) Cullen Prime Search</a>. %H A005849 Raphael M. Robinson, <a href="https://doi.org/10.1090/S0002-9939-1958-0096614-7">A Report on primes of the form k*2^n + 1 and on factors of Fermat numbers</a>, Proceedings of the American Mathematical Society, Vol. 9, No. 5 (1958), pp. 673-681. %H A005849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CullenNumber.html">Cullen Number</a>. %H A005849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>. %t A005849 Select[Range[1000], PrimeQ[# 2^# + 1] &] (* _Alonso del Arte_, Jul 30 2017 *) %o A005849 (PARI) is(n)=isprime(n<<n + 1) \\ _Charles R Greathouse IV_, Feb 06 2017 %Y A005849 Cf. A002064, A002234, A050920, A173474 (complement). %K A005849 hard,nonn,nice,more %O A005849 1,2 %A A005849 _N. J. A. Sloane_ %E A005849 a(14) = 1354828 from old Proth Search pages by Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 20 2006 %E A005849 The term 1467763 was added in error and has now been deleted; _Jens Kruse Andersen_, Nov 28 2007, remarks that 1467763 * 2^1467763 - 1 is a Woodall prime, but 3 divides the Cullen number 1467763 * 2^1467763 + 1. %E A005849 6328548 from John Blazek, May 14 2009. He later reports that the search of the range from 6300000 to 6328548 was completed on May 28 2009. %E A005849 Added a(16) = 6679881 from Caldwell's page, fixed broken link. - _M. F. Hasler_, Jan 18 2015 %E A005849 Name edited by _Andrey Zabolotskiy_ and _Felix Fröhlich_, May 28 2021