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A181172 Primes whose base 4 representation does not contain a 0. 1

%I

%S 2,3,5,7,11,13,23,29,31,37,41,43,47,53,59,61,89,101,103,107,109,127,

%T 149,151,157,167,173,181,191,223,229,233,239,251,347,349,359,367,373,

%U 379,383,409,421,431,439,443,479,487,491,503,509,599,601,607,613,617,619

%N Primes whose base 4 representation does not contain a 0.

%C This sequence contains all Mersenne primes (i.e. this is a supersequence of A000668). - _Iain Fox_, Dec 25 2017

%H Robert Israel, <a href="/A181172/b181172.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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))];

%p # Alternative:

%p 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

%t Select[Prime@ Range@ 120, DigitCount[#, 4, 0] == 0 &] (* _Michael De Vlieger_, Dec 24 2017 *)

%o (MAGMA) [ p: p in PrimesUpTo(620) | not exists(t){d: d in Intseq(p, 4) | d eq 0 } ]; // _Klaus Brockhaus_, Oct 10 2010

%o (PARI) lista(nn) = forprime(p=2, nn, if(!setsearch(Set(digits(p, 4)), 0), print1(p, ", "))) \\ _Iain Fox_, Dec 25 2017

%Y Cf. A082555, A000668 (subsequence).

%Y 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

%K base,nonn

%O 1,1

%A _Jonathan D. B. Hodgson_, Oct 08 2010

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Last modified July 25 10:05 EDT 2021. Contains 346289 sequences. (Running on oeis4.)