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 A235463 Primes whose base-6 representation also is the base-2 representation of a prime. 2
 7, 37, 43, 223, 1297, 1303, 1549, 7993, 9109, 46663, 54469, 55987, 326593, 1679659, 1681129, 1727569, 1734049, 1967587, 2006461, 2007763, 2014027, 2015287, 10077919, 10125649, 10125691, 10133467, 10412107, 10413397, 11757349, 11766421, 11766427, 11766637 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=6, thus a subsequence of A077720. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE 7 = 11_6 and 11_2 = 3 are both prime, so 7 is a term. 37 = 101_6 and 101_2 = 5 are both prime, so 37 is a term. MATHEMATICA b62Q[n_]:=Module[{idn6=IntegerDigits[n, 6]}, Max[idn6]<2&&AllTrue[ {FromDigits[ idn6, 6], FromDigits[idn6, 2]}, PrimeQ]]; Select[Prime[ Range[ 4, 780000]], b62Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 29 2020 *) PROG (PARI) is(p, b=2, c=6)=vecmax(d=digits(p, c))

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Last modified September 17 09:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)