A235144 Primes whose base-10 representation also represents a prime in base 19.

2, 3, 5, 7, 23, 29, 43, 47, 113, 131, 151, 157, 179, 199, 229, 263, 283, 311, 317, 353, 359, 409, 421, 443, 461, 557, 593, 641, 661, 739, 773, 809, 821, 881, 937, 953, 977, 1031, 1109, 1213, 1217, 1231, 1279, 1291, 1297, 1307, 1433, 1439, 1583, 1657, 1693, 1697, 1741, 1789, 1811, 1873, 1877, 1949, 1987, 2003

Offset: 1

Author

M. F. Hasler, Jan 03 2014

Keywords

• nonn
• base

Comments

See A090714 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 19, stands for 2*19 + 3 = 41, which is also prime, therefore 23 is in the sequence.
		

Links

• Robert Price, Table of n, a(n) for n = 1..3276

Crossrefs

Cf. A235110, A235126 and other sequences in the range A090707 - A091924.

Programs

Mathematica

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#], 19]] &] (* Alonso del Arte, Jan 04 2014 *)

PARI

is_A235144(p, b=19)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows one to produce similar sequences for other bases b > 9 (which can be given as optional 2nd argument), but does not do the required check for bases b < 10.