A090712 Primes whose base-13 expansion is a (valid) decimal expansion of a prime.

2, 3, 5, 7, 29, 53, 59, 79, 107, 113, 241, 263, 269, 293, 367, 373, 419, 443, 521, 523, 547, 601, 607, 631, 677, 757, 761, 787, 937, 971, 1021, 1069, 1093, 1231, 1249, 1277, 1307, 1361, 1381, 1433, 1459, 1543, 1567, 1613, 1619, 2213, 2237, 2239, 2447, 2477

Offset

1,1

Comments

See A235110 for a similar sequence whose definition works "in the opposite direction": Actually, the base-13 representation of the terms here. - M. F. Hasler, Jan 03 2014

Links

Robert Price, Table of n, a(n) for n = 1..14473

Example

The prime p = 53 is written 41 in base 13, and 41 is again (the base 10 representation of) a prime. Therefore p = 53 is a term of this sequence. [Rephrased by M. F. Hasler, Jan 03 2014]

Mathematica

f[n_]:=Module[{c13=FromDigits[IntegerDigits[n], 13]}, If[PrimeQ[c13], c13, 0]]; Select[f/@Prime[Range[500]], #!=0&] (* Harvey P. Dale, Jun 20 2011 *)

Prog

(PARI) is_A090712(p)=vecmax(d=digits(p, 13))<10&&isprime(vector(#d, i, 10^(#d-i))*d~)&&isprime(p) \\ M. F. Hasler, Jan 05 2014

Crossrefs

Cf. A090707 - A091924.

Sequence in context: A069108 A156604 A046864 * A082257 A054750 A048404

Adjacent sequences: A090709 A090710 A090711 * A090713 A090714 A090715

Keyword

base,nonn

Author

Cino Hilliard, Jan 18 2004

Extensions

Edited by N. J. A. Sloane, Feb 07 2007, and by M. F. Hasler, Jan 05 2014

Status

approved