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

1,1

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A082715 A133660 A271925 * A057663 A056244 A173487

Adjacent sequences: A236362 A236363 A236364 * A236366 A236367 A236368

Keyword

nonn,base

Author

K. D. Bajpai, Jan 23 2014

Status

approved