A236537 Primes whose binary and ternary representations are also prime when read in decimal.

157, 199, 229, 313, 367, 523, 883, 1483, 2683, 2971, 3109, 3253, 3637, 4093, 4357, 4363, 4729, 4951, 5119, 5827, 6529, 9241, 10909, 11527, 13477, 15271, 15919, 18439, 19273, 19483, 22921, 24019, 29833, 31237, 31573, 32803, 35863, 35899, 36109, 36973, 39799

Offset: 1

Author

K. D. Bajpai, Jan 28 2014

Keywords

• nonn
• base

Examples

			157 is prime and appears in the sequence. Its representation in binary = 10011101 and in ternary = 12211 are also prime when read in decimal.
313 is prime and appears in the sequence. Its representation in binary = 100111001 and in ternary = 102121 are also prime when read in decimal.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2115

Crossrefs

Cf. A000040 (prime numbers), A065720 (primes: binary representation is also prime), A236365 (primes: binary and octal representation is also prime), A236512 (primes: base 2, 3, 4 and 5 representation are also prime).

Programs

Mathematica

t={}; n=1; While[Length[t] < 50, n=NextPrime[n]; If[PrimeQ[FromDigits[IntegerDigits[n,2]]] && PrimeQ[FromDigits[IntegerDigits[n,3]]], AppendTo[t,n]]]; t

PARI

base_b(n, b) = my(s=[], r, x=10); while(n>0, r = n%b; n = n\b; s = concat(r, s)); eval(Pol(s))
s=[]; forprime(p=2, 40000, if(isprime(base_b(p, 2)) && isprime(base_b(p, 3)), s=concat(s, p))); s \\ Colin Barker, Jan 28 2014