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A090712 Primes whose base-13 expansion is a (valid) decimal expansion of a prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A069108 A156604 A046864 * A082257 A054750 A048404
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

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Last modified July 18 16:16 EDT 2024. Contains 374388 sequences. (Running on oeis4.)