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
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
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