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A235482
Primes whose base-5 representation is also the base-9 representation of a prime.
63
2, 3, 7, 11, 17, 19, 37, 41, 61, 67, 71, 97, 109, 131, 139, 149, 151, 157, 167, 191, 197, 211, 251, 269, 281, 337, 349, 367, 401, 409, 439, 449, 457, 467, 487, 491, 499, 521, 557, 569, 607, 619, 631, 647, 661, 739, 761, 769, 821, 829, 887, 907, 941, 947, 967, 1009, 1019, 1031, 1061, 1069, 1087
OFFSET
1,1
COMMENTS
This sequence is part of a two-dimensional array of sequences, given in the LINK, based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.
A subsequence of A197636 and of course of A000040A015919.
EXAMPLE
41 = 131_5 and 131_9 = 109 are both prime, so 41 is a term.
MATHEMATICA
Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 5], 9] &] (* Giovanni Resta, Sep 12 2019 *)
PROG
(PARI) is(p, b=9, c=5)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: Code only valid for b > c.
CROSSREFS
Cf. A235265, A235266, A235461 - A235481, A065720A036952, A065721 - A065727, A089971A020449, A089981, A090707 - A091924, A235394, A235395. See the LINK for further cross-references.
Sequence in context: A045323 A161185 A226993 * A375818 A155141 A127944
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 12 2014
STATUS
approved