A036955 - OEIS

%I #29 Jan 12 2019 21:17:40

%S 2,3,5,7,11,13,17,19,23,29,37,43,47,53,55,61,71,73,77,79,83,91,97,103,

%T 107,109,113,115,121,131,133,149,151,157,163,167,169,181,191,193,197,

%U 203,217,227,233,241,247,251,253,275,277,287,293,299,305,307,311,313

%N Numbers whose base-4 representation is the decimal representation of a prime.

%C All terms are congruent to 1 or 3 (mod 4) (except for the first one) and congruent to 1 or 5 (mod 6) (except for the first two); although not all terms are prime, as e.g., 55, 77, 91, 115, 121, 133, 169, 203, ... - _M. F. Hasler_, Jul 25 2015

%C Numbers (not necessarily prime) which are prime if written in base 4 and reinterpreted in base 10. Numbers n such that A007090(n) is in A000040. - _R. J. Mathar_, Jul 28 2015

%H Harvey P. Dale, <a href="/A036955/b036955.txt">Table of n, a(n) for n = 1..1000</a>

%e 55 is in the sequence because 55_10 = 313_4 and 313_10 is prime.

%e 313 is in the sequence because 313_10 = 10321_4 and 10321_10 is prime.

%e 31 is not in the sequence because 31_10 = 133_4 and 133_10 = 7*19 is not prime.

%t FromDigits[IntegerDigits[#],4]&/@Select[Prime[Range[2000]],Max[ IntegerDigits[ #]]<4&] (* _Harvey P. Dale_, May 02 2015 *)

%o (PARI) is(n)=isprime(sum(i=1,#n=digits(n,4),n[i]*10^(#n-i))) \\ _M. F. Hasler_, Jul 25 2015

%Y Cf. A004678, A036952 - A036964, A107715.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jan 04 1999

%E Offset corrected to 1 and minor edits by _M. F. Hasler_, Jul 25 2015