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%I #44 Mar 16 2023 08:50:52
%S 3,6,7,8,10,11,12,14,16,22,32,34,38,82,83,106,128,149,218,223,334,412,
%T 436,599,647,916,1373,4414,7246,8423,10118,10942,15898,42422,65986
%N Numbers k such that 2^k + 3^k is a semiprime.
%C Empirically, the smaller factor of 2^a(n) + 3^a(n) is a term of A294132 for all known terms. a(34) > 22000. - _Hugo Pfoertner_, Jul 29 2019
%C Terms for n >= 34 are probable semiprimes. - _Tyler Busby_, Feb 18 2023
%C Empirically, this sequence is a subsequence of A093641. No more terms of A093641 less than 10^5 are in this sequence. - _Tyler Busby_, Feb 20 2023
%H factordb, <a href="http://factordb.com/index.php?query=%283%5E42422%2B2%5E42422%29%2F13">Status of (3^42422+2^42422)/13</a>.
%e a(1)=3 because 2^3 + 3^3 = 5 * 7.
%e a(2)=6 because 2^6 + 3^6 = 13 * 61.
%e a(3)=7 because 2^7 + 3^7 = 5 * 463.
%e a(4)=8 because 2^8 + 3^8 = 17 * 401.
%e a(5)=10 because 2^10 + 3^10 = 13 * 4621.
%e a(6)=11 because 2^11 + 3^11 = 5 * 35839.
%e a(7)=12 because 2^12 + 3^12 = 97 * 5521.
%e a(8)=14 because 2^14 + 3^14 = 13 * 369181.
%e a(9)=16 because 2^16 + 3^16 = 3041 * 14177.
%e a(10)=22 because 2^22 + 3^22 = 13 * 2414250301.
%e a(11)=32 because 2^32 + 3^32 = 1153 * 1607133116929.
%e a(12)=34 because 2^34 + 3^34 = 13 * 1282861452271981.
%e a(13)=38 because 2^38 + 3^38 = 13 * 103911691734684541.
%e a(14)=82 because 2^82 + 3^82 = 13 * 102329189594547549657540565413396038701.
%e a(15)=83 because 2^83 + 3^83 = 5 * 798167678837469920188160718521149336927.
%e a(16)=106 because 2^106 + 3^106 = 13 * 28900785585664327723593061693364968422740414514061.
%e a(17)=128 because 2^128 + 3^128 = 257 * 45876204582640401445607833244277975113391731388650867226881.
%e a(18)=149 because 2^149 + 3^149 = 5 * 24665899002341798194980052306171212216360861465143461865961807325057879.
%Y Cf. A001358, A007689, A082101, A294132.
%K nonn,more,hard
%O 1,1
%A _Hugo Pfoertner_, May 08 2003
%E Corrected and extended by _Hugo Pfoertner_, May 12 2003
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007
%E a(28)-a(32) from _Sean A. Irvine_, Nov 05 2009
%E a(33) from _Hugo Pfoertner_, Jul 29 2019
%E a(34)-a(35) from _Tyler Busby_, Jan 14 2023