A077718 Primes which can be expressed as sum of distinct powers of 4.

5, 17, 257, 277, 337, 1093, 1109, 1297, 1301, 1361, 4177, 4357, 4373, 4421, 5189, 5381, 5393, 5441, 16453, 16657, 16661, 17477, 17489, 17669, 17681, 17729, 17749, 20549, 20753, 21521, 21569, 21589, 21841, 65537, 65557, 65617, 65809, 66629

Offset: 1

Author

Amarnath Murthy, Nov 19 2002

Keywords

• nonn

Comments

Primes whose base 4 representation contains only zeros and 1's.

As a subsequence of primes in A000695, these could be called Moser-de Bruijn primes. See also A235461 for those terms whose base 4 representation also represents a prime in base 2. - M. F. Hasler, Jan 11 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020449, A000695, A077717, A077719, A077720, A077721, A077722.

Programs

Maple

f:= proc(n) local L,x;
  L:= convert(n,base,2);
  x:= 1+add(L[i]*4^i,i=1..nops(L));
  if isprime(x) then x fi
end proc:
map(f, [$1..1000]); # Robert Israel, Sep 06 2018

Mathematica

Select[Prime[Range[6650]],Max[IntegerDigits[#,4]]<=1&] (* Jayanta Basu, May 22 2013 *)

PARI

for(i=1,999,isprime(b=vector(#b=binary(i),j,4^(#b-j))*b~)&&print1(b",")) \\ - M. F. Hasler, Jan 12 2014

Extensions

More terms from Sascha Kurz, Jan 03 2003