A075765 - OEIS

%I #11 Feb 17 2015 20:19:57

%S 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,

%T 26,25,26,7,7,9,7,13,11,13,15,15,17,19,17,23,21,21,19,27,35,35,33,33,

%U 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

%N a(n) = floor(prime(n)/n) + (prime(n) mod n).

%C The digital sum base n of the n-th prime. - _Hieronymus Fischer_, Dec 24 2007

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

%F a(n) = ds_n(prime(n)), where ds_n = digital sum base n. - _Hieronymus Fischer_, Oct 09 2007

%F 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

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

%t fmQ[n_]:=Module[{pn=Prime[n]},Floor[pn/n]+Mod[pn,n]]

%t fmQ/@Range[90]  (* _Harvey P. Dale_, Feb 25 2011 *)

%Y Cf. A007953.

%K nonn

%O 1,1

%A _Werner D. Sand_, Oct 09 2002

%E Corrected by _Hieronymus Fischer_, Oct 09 2007