A050244 Numbers k such that 2^k + 3^k is a semiprime.

3, 6, 7, 8, 10, 11, 12, 14, 16, 22, 32, 34, 38, 82, 83, 106, 128, 149, 218, 223, 334, 412, 436, 599, 647, 916, 1373, 4414, 7246, 8423, 10118, 10942, 15898, 42422, 65986

Offset: 1

Author

Hugo Pfoertner, May 08 2003

Keywords

• nonn
• more
• hard

Comments

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

Terms for n >= 34 are probable semiprimes. - Tyler Busby, Feb 18 2023

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

Examples

			a(1)=3 because 2^3 + 3^3 = 5 * 7.
a(2)=6 because 2^6 + 3^6 = 13 * 61.
a(3)=7 because 2^7 + 3^7 = 5 * 463.
a(4)=8 because 2^8 + 3^8 = 17 * 401.
a(5)=10 because 2^10 + 3^10 = 13 * 4621.
a(6)=11 because 2^11 + 3^11 = 5 * 35839.
a(7)=12 because 2^12 + 3^12 = 97 * 5521.
a(8)=14 because 2^14 + 3^14 = 13 * 369181.
a(9)=16 because 2^16 + 3^16 = 3041 * 14177.
a(10)=22 because 2^22 + 3^22 = 13 * 2414250301.
a(11)=32 because 2^32 + 3^32 = 1153 * 1607133116929.
a(12)=34 because 2^34 + 3^34 = 13 * 1282861452271981.
a(13)=38 because 2^38 + 3^38 = 13 * 103911691734684541.
a(14)=82 because 2^82 + 3^82 = 13 * 102329189594547549657540565413396038701.
a(15)=83 because 2^83 + 3^83 = 5 * 798167678837469920188160718521149336927.
a(16)=106 because 2^106 + 3^106 = 13 * 28900785585664327723593061693364968422740414514061.
a(17)=128 because 2^128 + 3^128 = 257 * 45876204582640401445607833244277975113391731388650867226881.
a(18)=149 because 2^149 + 3^149 = 5 * 24665899002341798194980052306171212216360861465143461865961807325057879.
		

Links

• factordb, Status of (3^42422+2^42422)/13.

Crossrefs

Cf. A001358, A007689, A082101, A294132.

Extensions

Corrected and extended by Hugo Pfoertner, May 12 2003

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007

a(28)-a(32) from Sean A. Irvine, Nov 05 2009

a(33) from Hugo Pfoertner, Jul 29 2019

a(34)-a(35) from Tyler Busby, Jan 14 2023