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Search: id:A065723
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| A065723 |
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Primes p such that the decimal expansion of its base 5 conversion is also prime. |
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+0
1
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| 2, 3, 13, 23, 41, 71, 83, 101, 163, 191, 211, 281, 283, 311, 331, 463, 503, 571, 613, 653, 701, 743, 823, 863, 881, 983, 1091, 1213, 1231, 1283, 1301, 1373, 1381, 1423, 1471, 1493, 1531, 1543, 1621, 1741, 1783, 1861, 1873, 1931, 2063, 2203, 2213, 2221
(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) = (5) [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. 2213{10} = 32323{5} is prime but also 32323{10}.
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MATHEMATICA
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Select[ Range[2250], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 5]]] & ]
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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, 5); if (isprime(b), write("b065723.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: A136260 A133201 A103150 this_sequence A024779 A087906 A029737
Adjacent sequences: A065720 A065721 A065722 this_sequence A065724 A065725 A065726
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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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