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Search: id:A065727
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| A065727 |
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Primes p such that the decimal expansion of its base 9 conversion is also prime. |
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+0
9
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| 2, 3, 5, 7, 37, 43, 61, 109, 127, 199, 271, 277, 379, 457, 487, 523, 541, 613, 619, 673, 727, 757, 883, 907, 919, 991, 997, 1033, 1117, 1249, 1447, 1483, 1531, 1549, 1567, 1627, 1693, 1699, 1747, 1753, 1987, 2053, 2161, 2221, 2287, 2341, 2347, 2437, 2473
(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) = (9) [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. 997{10} = 1327{9} is prime but also 1327{10}.
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MATHEMATICA
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Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ]
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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, 9); if (isprime(b), write("b065727.txt", n++, " ", p); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 28 2009]
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CROSSREFS
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Cf. A065720 up to A065726, A065361.
Sequence in context: A067907 A048415 A029974 this_sequence A090713 A090912 A048416
Adjacent sequences: A065724 A065725 A065726 this_sequence A065728 A065729 A065730
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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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