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 A235464 Primes whose base-7 representation also is the base-2 representation of a prime. 1
 7, 2801, 17207, 19559, 134513, 134807, 840743, 842759, 842801, 941249, 943601, 958007, 958049, 958343, 5899657, 6591089, 6607903, 6706393, 6722857, 41196751, 41311663, 41314057, 46137673, 46137967, 46253257, 46942351, 46944409, 47059657 (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=7, thus a subsequence of A077721. LINKS EXAMPLE 7 = 10_7 and 10_2 = 2 are both prime, so 7 is a term. 2801 = 11111_7 and 11111_2 = 31 are both prime, so 2801 is a term. PROG (PARI) is(p, b=2, c=7)=vecmax(d=digits(p, c))

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Last modified March 29 22:15 EDT 2023. Contains 361599 sequences. (Running on oeis4.)