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

1,1

Links

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

Example

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.

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

Prog

(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

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).

Sequence in context: A178092 A140035 A007356 * A048927 A343702 A163490

Adjacent sequences: A236534 A236535 A236536 * A236538 A236539 A236540

Keyword

nonn,base

Author

K. D. Bajpai, Jan 28 2014

Status

approved