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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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3
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3, 7, 31, 127, 3583, 8191, 131071, 524287, 14680063, 1073479679, 2147483647, 266287972351, 4260607557631, 17591112302591, 246290604621823, 17996806323437567, 1152917106560335871, 2305843009213693951
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OFFSET
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1,1
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COMMENTS
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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, Jan 22 2006
For all n with prime(n) < 300, a(n) has either prime(n) or prime(n)+1 bits. - David Wasserman, Oct 25 2006
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LINKS
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FORMULA
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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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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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