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A058249
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(Smallest prime >= 2^n) - (largest prime <= 2^n).
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10
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0, 2, 4, 4, 6, 6, 4, 6, 12, 10, 14, 6, 18, 30, 22, 16, 30, 8, 22, 10, 26, 18, 24, 46, 74, 20, 68, 60, 14, 38, 12, 20, 26, 66, 84, 36, 34, 52, 30, 102, 48, 26, 86, 24, 114, 36, 120, 80, 150, 82, 150, 68, 116, 192, 58, 86, 22, 96, 186, 126, 16, 192, 54, 72, 180, 14, 22, 56
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OFFSET
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1,2
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COMMENTS
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This sequence gives the gap between consecutive primes on either side of 2^n. The average gap between primes near 2^n should be about g=n*log(2). Cramer's conjecture would allow gaps to be as large as about g^2. - T. D. Noe, Jul 17 2007
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LINKS
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FORMULA
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EXAMPLE
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n = 1: a(1) = 2 - 2 = 0,
n = 9: a(9) = 521 - 509 = 12.
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MAPLE
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a := n -> if n > 1 then nextprime(2^n)-prevprime(2^n) else 0 fi; [seq( a(i), i=1..256)]; # Maple's next/prevprime functions use strict inequalities and therefore would not yield the correct difference for n=1. Alternatively, a(n) = nextprime(2^n-1)-prevprime(2^n+1);
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MATHEMATICA
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Prepend[NextPrime[#]-NextPrime[#, -1]&/@(2^Range[2, 70]), 0] (* Harvey P. Dale, Jan 25 2011 *)
Join[{0}, Table[NextPrime[2^n] - NextPrime[2^n, -1], {n, 2, 70}]]
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PROG
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CROSSREFS
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KEYWORD
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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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