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

1,1

Comments

See A090714 for a similar sequence whose definition works "in the opposite direction".

Links

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

Example

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.

Mathematica

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

Prog

(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.

Crossrefs

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

Sequence in context: A068690 A069556 A210110 * A235126 A382027 A309248

Adjacent sequences: A235141 A235142 A235143 * A235145 A235146 A235147

Keyword

nonn,base

Author

M. F. Hasler, Jan 03 2014

Status

approved