A235110 Primes whose base-10 representation also represents a prime in base 13.

2, 3, 5, 7, 23, 41, 47, 61, 83, 89, 157, 173, 179, 197, 223, 229, 263, 281, 311, 313, 331, 373, 379, 397, 401, 463, 467, 487, 571, 599, 607, 643, 661, 739, 751, 773, 797, 809, 823, 863, 883, 919, 937, 971, 977

Offset: 1

Author

M. F. Hasler, Jan 03 2014

Keywords

• nonn
• base

Comments

See A090712 for a similar sequence whose definition works "in the opposite direction".

Examples

			The decimal representation of prime 23, considered as a number written in base 13, stands for 2*13+3 = 29, which is also prime, therefore 23 is in the sequence.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A235110, A235144 and other sequences in the range A090707 - A091924.

Programs

Mathematica

Select[Prime[Range[5000]],PrimeQ[FromDigits[IntegerDigits[#],13]]&] (* Zak Seidov, Aug 31 2015 *)

PARI

is_A235110(p, b=13)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)}