A004051 Primes of the form 2^a + 3^b.

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 67, 73, 83, 89, 97, 113, 131, 137, 251, 257, 283, 307, 337, 499, 521, 593, 733, 761, 857, 1033, 1051, 1753, 2129, 2203, 2251, 2699, 2777, 4099, 4177, 4339, 6563, 6569, 6577, 6689, 8219, 8273, 8609, 10657, 14753

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Are a(3)=5, a(5)=11 and a(7)=17 the only cases with two ways of representation: {5=2^2+3^0=2^1+3^1, 11=2^3+3^1=2^1+3^2, 17=2^4+3^0=2^3+3^2}? - Zak Seidov, Feb 24 2015

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Zak Seidov, Corresponding values of a and b.

Crossrefs

Cf. A010051, subsequence of A004050.

Programs

Haskell

a004051 n = a004051_list !! (n-1)
a004051_list = filter ((== 1) . a010051'') a004050_list
-- Reinhard Zumkeller, May 20 2015

MATLAB

n = 0; for a = 0:30 p1 = 2^a; for b = 0:19; p2 = 3^b; p3 = p1 + p2; if isprime(p3) n = n + 1; c(n) = p3; end; end; end; c = sort(c); k = size(c, 2); for i = 2:k if c(i-1) == c(i) c(i-1) = 0 end; end; c = sort(c); c = sym(c) % Lei Zhou, Jan 26 2005

Mathematica

nMax = 15000; Union[Select[2^First[#] + 3^Last[#] & /@ Tuples[{Range[0, Log[2, nMax]], Range[0, Log[3, nMax]]}], # <= nMax && PrimeQ[#] &]]  (* Harvey P. Dale, Mar 13 2011 *)