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Primes whose binary and ternary representations are also prime when read in decimal.
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%I #23 Jul 19 2016 11:39:41

%S 157,199,229,313,367,523,883,1483,2683,2971,3109,3253,3637,4093,4357,

%T 4363,4729,4951,5119,5827,6529,9241,10909,11527,13477,15271,15919,

%U 18439,19273,19483,22921,24019,29833,31237,31573,32803,35863,35899,36109,36973,39799

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

%H K. D. Bajpai, <a href="/A236537/b236537.txt">Table of n, a(n) for n = 1..2115</a>

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

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

%t 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

%o (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))

%o 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

%Y 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).

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 28 2014