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A166597
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Let p = largest prime <= n, with p(0)=p(1)=0, and let q = smallest prime > n; then a(n) = q-p.
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2
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2, 2, 1, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 2, 2, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 2, 2, 4, 4
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OFFSET
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0,1
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COMMENTS
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Note the large prime gap of 72 between 31397 and 31469. This is the prime gap with the largest merit (cf. A111870), 72/log(31397)=6.95352 for primes less than 100000. Also 72/(log(31397))^2=0.67154 (cf. conjectures of Cramer-Granville, Shanks and Wolf) is largest for primes less than 100000. - Daniel Forgues, Oct 23 2009
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LINKS
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Eric Weisstein's World of Mathematics, Prime Gaps.
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EXAMPLE
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a(0) = 2 since the least prime greater than 0 is 2 (gap of 2 from 0 to 2).
a(9) = 4 since the least prime greater than 9 is 11 (gap of 4 from 7 to 11).
a(11) = 2 since the least prime greater than 11 is 13 (gap of 2 from 11 to 13).
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MATHEMATICA
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f[n_]:=Module[{a=If[PrimeQ[n], n, NextPrime[n, -1]]}, NextPrime[n]-a]; Join[{2, 2}, Array[f, 120, 2]] (* Harvey P. Dale, May 17 2011 *)
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PROG
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(PARI) a(n) = nextprime(n+1) - precprime(n); \\ Michel Marcus, Mar 02 2023
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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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