A072923 Number of primes of the form floor( (1+1/k)^n ), 1<=k<=n.

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

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Mathematica

a[n_] := Count[Floor[(1 + 1/Range[n])^n], _?PrimeQ]; Array[a, 100] (* Amiram Eldar, Aug 28 2020 *)

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