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

Author

Werner D. Sand, Oct 09 2002

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A007953.

Programs

Mathematica

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

Formula

p(n)/n = k + r; r

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

Extensions

Corrected by Hieronymus Fischer, Oct 09 2007

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