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A235467
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Primes whose base-4 representation also is the base-3 representation of a prime.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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E.g., 89 = 1121_4 and 1121_3 = 43 both are prime.
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(p, b=3, c=4)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 4, 3)&&print1(vector(#d=digits(p, 3), i, 4^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 4)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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