

A236537


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 A163490 A142063
Adjacent sequences: A236534 A236535 A236536 * A236538 A236539 A236540


KEYWORD

nonn,base


AUTHOR

K. D. Bajpai, Jan 28 2014


STATUS

approved



