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

1,1

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

Links

Table of n, a(n) for n=1..35.

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

Example

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.

Crossrefs

Cf. A001358, A007689, A082101, A294132.

Sequence in context: A168114 A220656 A324143 * A295566 A266986 A047283

Adjacent sequences: A050241 A050242 A050243 * A050245 A050246 A050247

Keyword

nonn,more,hard

Author

Hugo Pfoertner, May 08 2003

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

Status

approved