Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Mar 31 2012 13:20:33
%S 5,17,37,-1,101
%N Smallest generalized Fermat prime of the form (2n)^(2^k) + 1, where k>0; or -1 if no such prime exists.
%C a(n) = -1 for n = {4, 16, 32, 64, 108, 256, 500, ...}.
%C All primes of the form 4*n^2 + 1 belong to a(n). They are listed in A121326(n).
%C Last digit of a(5k)>0 is 1.
%C Last digit of a(n)>0 is 7 if k is not congruent to 0 mod 5, except a(1) = 5.
%C All currently known a(n) for 6<n<100 are listed below:
%C a(7)-a(8) = {197, 257}. a(10) = 401.
%C a(12)-a(18) = {577, 677, 614657, 185302018885184100000000000000000000000000000001, -1, 1336337, 1297}.
%C a(20) = 1601. a(22)-a(24) = {197352587024076973231046657, 4477457, 5308417}.
%C a(27)-a(28) = {2917, 3137}. a(32)-a(33) = {-1, 4357}.
%C a(37)-a(38) = {5477, 1238846438084943599707227160577}. a(40)-a(42) = {40960001, 45212177, 7057}.
%C a(44)-a(45) = {59969537, 8101}. a(47)-a(48) = {8837, 2708192040014184559945134363758220403329915059847434832829218817}.
%C a(51) = 355149324327687480512960334807820417442703411649746143408158197478603636302066719166373229531510062746472251495292613758147362817.
%C a(53) = 126247697.
%C a(55)-a(60) = {12101, 375817263084708503965641077546115954135779496817219617550715846657, 662148260948741787228316709317924977225312314678010411233675575297, 13457, 193877777, 14401}.
%C a(62)-a(67) = {153777, 15877, -1, 16901, 303595777, 17957}.
%C a(70)-a(71) = {384160001, 406586897}. a(73) = 21317.
%C a(75)-a(82) = {22501, 284936905588473857, 562448657, 24337, 150838912030874130174020868290707457, 25601, 2564253345083631031816684000763319514758972657894465952263290175258003723567069899841752707150583949000981132009709206360818037538528413351937, 723394817}.
%C a(85) = 28901. a(87)-a(88) = {916636177, 30977}. a(90) = 32401.
%C a(92) = 33857.
%C a(94)-a(95) = {2435149272410363768730097404205858817, 4791383378576850493153910080681360672521575296790233332710625780023370220270083429409686634957161195934369337557766908660231890537157173340981965932463779247224064100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001}.
%C a(97) = 1416468497. a(99) = 1536953617.
%C a(n) is currently unknown for n = {6, 9, 11, 19, 21, 25, 26, 29, 30, 31, 34, 35, 36, 39, 43, 46, 49, 50, 52, 54, 61, 68, 69, 72, 74, 83, 84, 86, 89, 91, 93, 96, 98, 100, ...}.
%H Jeppe Stig Nielsen, <a href="http://jeppesn.dk/generalized-fermat.html">Generalized Fermat Primes sorted by base</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>.
%Y Cf. A121326.
%K hard,more,sign
%O 1,1
%A _Alexander Adamchuk_, Nov 15 2006