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 A235462 Primes whose base-5 representation also is the base-2 representation of a prime. 2
 5, 31, 131, 151, 631, 3251, 3881, 19531, 78781, 78901, 81281, 81401, 81901, 82031, 94531, 97001, 97501, 390781, 394501, 406381, 469501, 471901, 472631, 484531, 1953901, 1956881, 1968751, 1969531, 1971901, 2031251, 2035151, 2046901, 2047651, 2050031, 2347001, 2360131 (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 he 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=5, thus a subsequence of A077719. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE 5 = 10_5 and 10_2 = 2 are both prime, so 5 is a term. 31 = 111_5 and 111_2 = 7 are both prime, so 31 is a term. MATHEMATICA b5b2Q[n_]:=Module[{idn5=IntegerDigits[n, 5]}, Max[idn5]<2 && PrimeQ[ FromDigits[ idn5, 2]]]; Select[Prime[Range[180000]], b5b2Q] (* Harvey P. Dale, Sep 21 2018 *) PROG (PARI) is(p, b=2, c=5)=vecmax(d=digits(p, c))

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Last modified September 22 08:15 EDT 2021. Contains 347605 sequences. (Running on oeis4.)