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 A235626 Primes whose base 6 representation also is the base 5 representation of a prime. 2
 2, 3, 13, 43, 97, 223, 307, 337, 379, 433, 457, 547, 709, 727, 769, 811, 919, 1009, 1303, 1597, 1609, 1777, 1861, 1987, 2017, 2029, 2221, 2239, 2269, 2311, 2647, 2689, 2749, 2917, 3037, 3067, 3121, 3169, 3373, 3529, 3541, 3571, 3613, 3967, 4219, 4261, 4327, 4339 (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. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE E.g., 13 = 21[6] and 21[5] = 11 both are prime. MAPLE P:= {seq(ithprime(i), i=1..10000)}: f:= proc(p) local i, L;   L:= convert(p, base, 5);   add(L[i]*6^(i-1), i=1..nops(L)) end proc: sort(convert(map(f, P) intersect P, list)); # Robert Israel, Jun 18 2019 MATHEMATICA b65pQ[n_]:=Module[{idn6=IntegerDigits[n, 6]}, Max[idn6]<5&&PrimeQ[ FromDigits[ idn6, 5]]]; Select[Prime[Range[600]], b65pQ] (* Harvey P. Dale, Oct 13 2020 *) PROG (PARI) is(p, b=5, c=6)=vecmax(d=digits(p, c))

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)