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Search: id:A093535
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| A093535 |
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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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+0
2
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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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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;
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.
Sequence in context: A001348 A006515 A081093 this_sequence A057612 A136005 A088552
Adjacent sequences: A093532 A093533 A093534 this_sequence A093536 A093537 A093538
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KEYWORD
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base,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 14 2004
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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
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