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A077718
Primes which can be expressed as sum of distinct powers of 4.
13
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
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 19 2002
EXTENSIONS
More terms from Sascha Kurz, Jan 03 2003
STATUS
approved