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Search: id:A081093
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| A081093 |
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a(n) is the smallest prime such that the number of 1's in its binary expansion is equal to the n-th prime. |
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4
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| 3, 7, 31, 127, 3583, 8191, 131071, 524287, 14680063, 1073479679, 2147483647, 266287972351, 4260607557631, 17591112302591, 246290604621823, 17996806323437567, 1152917106560335871, 2305843009213693951
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) = Min{p: A000120(p)=A000040(n), p prime}.
If 2^(Prime[n]) - 1 is a prime number, then a(n) = 2^(Prime[n]) - 1, where Prime[n] denotes the n-th prime number. This means that every Mersenne prime arises in this sequence. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jan 22 2006
For all n with prime(n) < 300, a(n) has either prime(n) or prime(n)+1 bits. - David Wasserman (dwasserm(AT)earthlink.net), Oct 25 2006
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FORMULA
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a(n) = A061712(A000040(n)). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 06 2006
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EXAMPLE
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n=4, p[4]=11, 3583=[11011111111] has 11 digits=1 and is prime;
2047=23.89=[11111111111] is not here because it is composite.
a(5)=3583=A081092(266)=A000040(502) having eleven 1's: '110111111111' and A000120(p)<11=prime(5) for primes p<3583.
Mersenne-primes are here, Mersenne composites not.
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MATHEMATICA
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Do[k=1; While[Count[IntegerDigits[Prime[k], 2], 1] !=Prime[n], k++ ]; Print[Prime[k]], {n, 1, 10}]
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CROSSREFS
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Cf. A000043, A000668, A001348, A061712, A000120, A014499.
Cf. A000040, A000120, A081092.
Sequence in context: A001348 A006515 A093535 this_sequence A057612 A136005 A088552
Adjacent sequences: A081090 A081091 A081092 this_sequence A081094 A081095 A081096
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KEYWORD
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base,nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 05 2003
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 06 2006
Further terms from David Wasserman (dwasserm(AT)earthlink.net), Oct 25 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2008 at the suggestion of R. J. Mathar
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