A181172 Primes whose base 4 representation does not contain a 0.

2, 3, 5, 7, 11, 13, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 89, 101, 103, 107, 109, 127, 149, 151, 157, 167, 173, 181, 191, 223, 229, 233, 239, 251, 347, 349, 359, 367, 373, 379, 383, 409, 421, 431, 439, 443, 479, 487, 491, 503, 509, 599, 601, 607, 613, 617, 619

Offset: 1

Author

Jonathan D. B. Hodgson, Oct 08 2010

Keywords

• base
• nonn

Comments

This sequence contains all Mersenne primes (i.e. this is a supersequence of A000668). - Iain Fox, Dec 25 2017

Examples

			53 = 311 (base 4), which contains no 0.
		

Links

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

Crossrefs

Cf. A082555, A000668 (subsequence).

Cf. A073779 (number of 0's in base-3 representation of n-th prime), A181173 (primes whose base 5 representation does not contain a 0). - Klaus Brockhaus, Oct 10 2010

Programs

Magma

[ p: p in PrimesUpTo(620) | not exists(t){d: d in Intseq(p, 4) | d eq 0 } ]; // Klaus Brockhaus, Oct 10 2010

Maple

The following code will store the first 200 terms into a sequence K. for i from 1 to 200 do if i=i then x[i]:=convert(ithprime(i),base,4) else x[i]:=0 end if: end do: S:={}: for i from 1 to 200 do if evalb(`in`(0, x[i]))=false then S:=S union {i} fi od; for i from 1 to nops(S)do z[i]:=ithprime(S[i]) od: K:=[seq((z[i]),i=1..nops(S))];
# Alternative:
select(t -> isprime(t) and not has(convert(t,base,4),0), [2,seq(i,i=3..10^4,2)]); # Robert Israel, Dec 24 2017

Mathematica

Select[Prime@ Range@ 120, DigitCount[#, 4, 0] == 0 &] (* Michael De Vlieger, Dec 24 2017 *)

PARI

lista(nn) = forprime(p=2, nn, if(!setsearch(Set(digits(p, 4)), 0), print1(p, ", "))) \\ Iain Fox, Dec 25 2017