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A038606
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Least k such that k-th prime > n * k.
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7
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1, 5, 12, 31, 69, 181, 443, 1052, 2701, 6455, 15928, 40073, 100362, 251707, 637235, 1617175, 4124437, 10553415, 27066974, 69709680, 179992909, 465769803, 1208198526, 3140421716, 8179002096, 21338685407, 55762149030, 145935689361, 382465573483, 1003652347100
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OFFSET
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1,2
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COMMENTS
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Numbers n such that prime(n) (mod n) begins the next cycle of terms in A004648. Generally prime(i) (mod i) exceeds prime(i-1) (mod i-1) but there are numerous times where for a short run prime(i) (mod i) is minimally less than its predecessor. Here n is substantially less. See Labos's graph.
With offset 2: Index j of prime p(j) such that ceiling[p(j)/j]=n is first satisfied. a(n) = A062742(n) = A038624(n) for n >= 3. [From Jaroslav Krizek, Dec 13 2009]
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LINKS
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FORMULA
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MAPLE
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for k from 1 do
if ithprime(k)> n*k then
return k;
end if;
end do:
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MATHEMATICA
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k = 1; Do[ While[ Floor[ Prime[k]/k] < n, k++ ]; Print[k]; k++, {n, 1, 30} ]
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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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Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul
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EXTENSIONS
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STATUS
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approved
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