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A039731
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a(n) = max{prime(n) mod q, where prime q < prime(n) = n-th prime}.
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3
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1, 2, 2, 4, 6, 6, 8, 10, 12, 14, 18, 18, 20, 18, 24, 28, 30, 30, 34, 36, 38, 40, 42, 44, 48, 50, 48, 50, 54, 60, 64, 66, 68, 70, 72, 78, 80, 78, 84, 82, 84, 94, 96, 96, 98, 104, 110, 100, 102, 106, 112, 114, 124, 126, 126, 132, 134, 138, 132, 134, 144, 150
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OFFSET
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2,2
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COMMENTS
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If there is a prime q with p/2 < q < 2p/3, then p mod q = p - q and a(n) = p - nextprime(p/2). But by a result of Nagura, there is always a prime between x and 6x/5 for x > 25, so this holds for all p > 50 and (checking 2 <= n <= 15) for all n > 1. - Charles R Greathouse IV, Jul 12 2024
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LINKS
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FORMULA
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a(n) = p - nextprime(p/2), where p is the n-th prime, see Greathouse comment. - Charles R Greathouse IV, Jul 12 2024
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MAPLE
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a := proc(n) ithprime(n); % - nextprime(iquo(%, 2)) end: seq(a(n), n = 2..63);
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MATHEMATICA
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PROG
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(PARI) a(n)=maxp = 0; for (i = 1, n-1, mp = prime(n) % prime(i); maxp = max(mp, maxp); ); maxp; \\ Michel Marcus, Oct 01 2013
(PARI) P=primes(100); vector(#P, i, mx=0; for(j=1, i-1, mx=max(P[i]%P[j], mx)); mx)[2..#P] \\ Charles R Greathouse IV, Oct 01 2013
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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