A075765 a(n) = floor(prime(n)/n) + (prime(n) mod n).

2, 2, 3, 4, 3, 3, 5, 5, 7, 11, 11, 4, 5, 4, 5, 8, 11, 10, 13, 14, 13, 16, 17, 20, 25, 26, 25, 26, 25, 26, 7, 7, 9, 7, 13, 11, 13, 15, 15, 17, 19, 17, 23, 21, 21, 19, 27, 35, 35, 33, 33, 35, 33, 39, 41, 43, 45, 43, 45, 45, 43, 49, 59, 59, 57, 57, 67, 69, 7, 73, 73, 75, 7, 8, 9, 8, 9, 12

Offset

1,1

Comments

The digital sum base n of the n-th prime. - Hieronymus Fischer, Dec 24 2007

Links

Table of n, a(n) for n=1..78.

Formula

p(n)/n = k + r; r<n; a(n) = k + r; p prime, n, k, r integers.

a(n) = ds_n(prime(n)), where ds_n = digital sum base n. - Hieronymus Fischer, Oct 09 2007

a(n) = prime(n) - (n-1)*sum_{k>0} floor(prime(n)/n^k) = prime(n) - (n-1)*floor(prime(n)/n). - Hieronymus Fischer, Oct 09 2007

Example

p(9)/9=23/9=2+5/9; a(9)=2+5=7

Mathematica

fmQ[n_]:=Module[{pn=Prime[n]}, Floor[pn/n]+Mod[pn, n]]
fmQ/@Range[90]  (* Harvey P. Dale, Feb 25 2011 *)

Crossrefs

Cf. A007953.

Sequence in context: A054703 A048206 A290740 * A309899 A181024 A214744

Adjacent sequences: A075762 A075763 A075764 * A075766 A075767 A075768

Keyword

nonn

Author

Werner D. Sand, Oct 09 2002

Extensions

Corrected by Hieronymus Fischer, Oct 09 2007

Status

approved