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A235469
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Primes whose base-6 representation also is the base-3 representation of a prime.
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2
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2, 13, 43, 73, 223, 1777, 2593, 2887, 3037, 3067, 3109, 7993, 9157, 9337, 10597, 17077, 17107, 17137, 17317, 17359, 18229, 18661, 46663, 48247, 49297, 49537, 54517, 54727, 54877, 54907, 54949, 55987, 56197, 56209, 56239, 57097, 63589, 63727, 64879, 65089, 65101, 95089, 95917, 96157
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OFFSET
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1,1
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COMMENTS
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This sequence is part of the two-dimensional array of sequences 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.
For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
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LINKS
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EXAMPLE
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E.g., 13 = 21_6 and 21_3 = 7 are both prime.
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PROG
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(PARI) is(p, b=3, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 6, 3)&&print1(vector(#d=digits(p, 3), i, 6^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 6)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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