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A038606 Least k such that k-th prime > n * k. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Log(a(n)) =~ -1.295 + 0.964312n. - Robert G. Wilson v, Jan 25 2002

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.

A090973(a(n)) = n+1. [From Reinhard Zumkeller, Aug 16 2009]

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]

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..50

Labos, E. Graph of first 50000 terms of A004648

Andrew R. Booker, The Nth Prime Page

FORMULA

a(n) = pi(A038607(n)) = A000720(A038607(n)).

MAPLE

A038606 := proc(n)

    for k from 1 do

        if ithprime(k)> n*k then

            return k;

        end if;

    end do:

end proc: # R. J. Mathar, Aug 24 2013

MATHEMATICA

k = 1; Do[ While[ Floor[ Prime[k]/k] < n, k++ ]; Print[k]; k++, {n, 1, 30} ]

PROG

(PARI) k=1; n=1; forprime(p=3, 4e9, if(p/n++>k, print1(n", "); k++)) \\ Charles R Greathouse IV, Sep 06 2011

CROSSREFS

Cf. A038607, A004648, A038625.

Sequence in context: A015625 A038357 A090974 * A192303 A301785 A066280

Adjacent sequences:  A038603 A038604 A038605 * A038607 A038608 A038609

KEYWORD

nonn

AUTHOR

Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul

EXTENSIONS

Edited by Robert G. Wilson v, Jan 25 2002

a(21)=179992909 corrected by Ray Chandler, Dec 01 2004

a(29)-a(30) from Charles R Greathouse IV, Sep 06 2011

a(31)-a(50) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Sep 01 2018

STATUS

approved

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Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)