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

1,1

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A281504 A191500 A089894 * A235461 A271660 A273948

Adjacent sequences: A077715 A077716 A077717 * A077719 A077720 A077721

Keyword

nonn

Author

Amarnath Murthy, Nov 19 2002

Extensions

More terms from Sascha Kurz, Jan 03 2003

Status

approved