A236365 Primes whose binary and octal representation are also prime when read in decimal.

3, 5, 89, 179, 199, 367, 383, 443, 523, 659, 947, 1097, 1163, 1289, 1483, 1753, 2351, 2423, 2903, 3041, 3217, 3299, 3631, 4729, 4951, 5119, 5347, 5879, 6007, 6131, 6491, 6911, 7547, 7577, 7649, 8167, 8849, 9241, 9511, 9817, 9929, 10303, 10831, 11251, 11527

Offset: 1

Author

K. D. Bajpai, Jan 23 2014

Keywords

• nonn
• base

Examples

			89 is prime and appears in the sequence:  89 in binary = 1011001 and in octal = 131, which are also prime when read in decimal.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1008

Crossrefs

Cf. A000040 (prime numbers), A065720 (primes: binary representation is also prime).

Programs

Maple

KD := proc() local a,b,d; a:=ithprime(n);  b:=convert(a, binary); d:=convert(a,octal); if isprime(b) and isprime(d) then RETURN (a) ;fi;  end: seq(KD(), n=1..50);

Mathematica

t = {}; n = 1; While[Length[t] < 50, n = NextPrime[n]; If[PrimeQ[FromDigits[IntegerDigits[n, 8]]] && PrimeQ[FromDigits[IntegerDigits[n, 2]]], AppendTo[t, n]]]; t (* T. D. Noe, Jan 26 2014 *)
 Select[Prime[Range[1400]],AllTrue[FromDigits/@{IntegerDigits[ #,2],IntegerDigits[ #,8]},PrimeQ]&](* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 30 2018 *)