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A235476
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Primes whose base-2 representation also is the base-6 representation of a prime.
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1
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3, 5, 7, 11, 17, 19, 29, 41, 53, 67, 101, 127, 193, 263, 281, 337, 353, 431, 461, 479, 487, 499, 523, 593, 599, 631, 743, 757, 773, 821, 823, 829, 857, 883, 887, 941, 1013, 1021, 1093, 1117, 1259, 1279, 1303, 1367, 1373, 1429, 1439, 1459, 1471, 1483, 1493, 1511, 1583, 1619, 1699, 1759, 1831, 1847, 1879, 1931, 1951, 1987
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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 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.
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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5 = 101_2 and 101_6 = 37 are both prime, so 5 is a term.
7 = 111_2 and 111_6 = 43 are both prime, so 7 is a term.
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MATHEMATICA
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Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 2], 6]]&] (* Harvey P. Dale, Jan 03 2022 *)
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PROG
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(PARI) is(p, b=6)=isprime(vector(#d=binary(p), i, b^(#d-i))*d~)&&isprime(p)
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CROSSREFS
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Cf. A235463 ⊂ A077720, A235475, A152079, A235266, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.
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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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