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Search: id:A065724
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| A065724 |
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Primes p such that the decimal expansion of its base 6 conversion is also prime. |
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+0
1
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| 2, 3, 5, 7, 19, 37, 67, 79, 97, 103, 127, 157, 163, 193, 229, 283, 307, 337, 439, 487, 547, 571, 601, 631, 643, 673, 733, 751, 757, 853, 877, 907, 937, 1021, 1033, 1039, 1087, 1093, 1117, 1171, 1249, 1279, 1423, 1567, 1627, 1663, 1723, 1753, 1831, 1873
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In general rebase notation (Marc LeBrun): p(n) = (6) [p] (10).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
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E.g. 1627{10} = 11311{6} is prime but also 11311{10}.
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MATHEMATICA
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Select[ Range[1900], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 6]]] & ]
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PROGRAM
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(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 6); if (isprime(b), write("b065724.txt", n++, " ", p); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 27 2009]
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CROSSREFS
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Cf. A065720 up to A065727, A065361.
Sequence in context: A087562 A154525 A144561 this_sequence A117315 A158473 A048420
Adjacent sequences: A065721 A065722 A065723 this_sequence A065725 A065726 A065727
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 2001.
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