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Search: id:A065720
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| A065720 |
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Primes p such that the decimal expansion of its base 2 conversion is also prime. |
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+0
11
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| 3, 5, 23, 47, 89, 101, 149, 157, 163, 173, 179, 199, 229, 313, 331, 367, 379, 383, 443, 457, 523, 587, 631, 643, 647, 653, 659, 709, 883, 947, 997, 1009, 1091, 1097, 1163, 1259, 1277, 1283, 1289, 1321, 1483, 1601, 1669, 1693, 1709, 1753, 1877
(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) = (2) [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. 1009{10} = 1111110001{2} is prime but also 1111110001{10}.
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MATHEMATICA
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Select[ Range[1900], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 2]]] & ]
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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, 2); if (isprime(b), write("b065720.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. A065721 up to A065727, A065361.
Sequence in context: A163153 A091157 A036952 this_sequence A148554 A120937 A075307
Adjacent sequences: A065717 A065718 A065719 this_sequence A065721 A065722 A065723
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KEYWORD
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nonn,base,new
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 15 2001.
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