

A072923


Number of primes of the form floor( (1+1/k)^n ) 1<=k<=n.


0



1, 1, 2, 3, 3, 5, 5, 4, 6, 5, 8, 5, 7, 6, 7, 7, 10, 8, 9, 8, 11, 12, 10, 12, 14, 10, 15, 13, 13, 17, 16, 16, 17, 14, 18, 18, 17, 22, 18, 22, 16, 21, 23, 20, 20, 24, 22, 24, 26, 23, 23, 26, 25, 26, 25, 28, 25, 31, 29, 26, 31, 27, 28, 31, 32, 31, 37, 32, 29, 32, 34, 31, 35, 34, 32
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


LINKS

Table of n, a(n) for n=1..75.


FORMULA

Conjecture: a(n) is asymptotic to C*n with C = 0.47......


EXAMPLE

floor((1+1/k)^15 is prime for k = 7,8,11,12,13,14,15 (giving the successive prime values 7,5,3,3,3,2,2) hence a(15)=7


PROG

(PARI) a(n)=if(n<0, 0, sum(k=1, n, if(isprime(floor((1+1/k)^n)), 1, 0)))


CROSSREFS

Sequence in context: A081768 A273493 A193404 * A257003 A131922 A260718
Adjacent sequences: A072920 A072921 A072922 * A072924 A072925 A072926


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Aug 11 2002


STATUS

approved



