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 A235467 Primes whose base-4 representation also is the base-3 representation of a prime. 2
 2, 89, 137, 149, 281, 293, 353, 389, 409, 421, 593, 613, 661, 1097, 1109, 1289, 1301, 1321, 1381, 1409, 1601, 1609, 1669, 2069, 2129, 2309, 2377, 2389, 2729, 4133, 4229, 4373, 4441, 4513, 4673, 5153 (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. This is a subsequence of A002144, A002313, A003655, A050150, A062090, A141293, A175768, A192592, A226181 (conjectural). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime EXAMPLE E.g., 89 = 1121_4 and 1121_3 = 43 both are prime. MATHEMATICA b4b3Q[n_]:=Module[{b4=IntegerDigits[n, 4]}, Max[b4]<3&&PrimeQ[ FromDigits[ b4, 3]]]; Select[Prime[Range[700]], b4b3Q] (* Harvey P. Dale, Dec 14 2021 *) PROG (PARI) is(p, b=3, c=4)=vecmax(d=digits(p, c))

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Last modified July 25 03:22 EDT 2024. Contains 374586 sequences. (Running on oeis4.)