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A235626
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Primes whose base-6 representation also is the base-5 representation of a prime.
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2
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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
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refs;
listen;
history;
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internal format)
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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.
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LINKS
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EXAMPLE
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Both 13 = 21_6 and 21_5 = 11 are prime.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(p, b=5, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 6, 5)&&print1(vector(#d=digits(p, 5), i, 6^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 6)
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CROSSREFS
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Cf. A235625, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.
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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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