A239926 3^(p-1)-2^(p+1) for primes p > 3.

17, 473, 54953, 515057, 42784577, 386371913, 31364282393, 22875718713137, 205886837127353, 150094360419092177, 12157661061010417697, 109418971539326314793, 8862937838177524385273, 6461081871212274789450257, 4710128696093323330314756713

Offset: 1

Author

Vincenzo Librandi, Jun 17 2014

Keywords

• nonn
• easy
• less

Comments

3^(p-1)-2^(p+1) can be written as (3^((p-1)/2)-2^((p+1)/2))*(3^((p-1)/2)+2^((p+1)/2)). Since 3^((p-1)/2)-2^((p+1)/2) > 1 for p > 5, these numbers are all composite after 17 = (3^2-2^3)*(3^2+2^3).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000040, A003063, A135171 (numbers of the form 3^p-2^p with p prime), A214091 (supersequence).

Programs

Magma

[3^(p-1)-2^(p+1): p in PrimesInInterval(4,100)];

Mathematica

Table[3^(Prime[n] - 1) - 2^(Prime[n] + 1), {n, 3, 100}]