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

Author

Cino Hilliard, Jan 18 2004

Keywords

• base
• nonn

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

Examples

			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]
		

Links

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

Crossrefs

Cf. A090707 - A091924.

Programs

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 *)

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

Extensions

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