A088673 - OEIS

%I #12 Nov 07 2024 15:47:50

%S 0,0,1,1,2,0,3,0,1,2,1,2,3,4,0,4,5,0,1,2,3,1,2,3,4,5,6,0,5,6,7,0,1,2,

%T 3,4,1,2,3,4,5,6,7,8,0,6,7,8,9,0,1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,0,7,8,

%U 9,10,11,0,1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,0,8,9,10,11,12,13,0,1,2

%N a(n) = n mod A002024(n), where A002024 is "n appears n times": 1, 2, 2, 3, 3, 3, ...

%e a(7) = 3: A002024(7) = 4 and 7 mod 4 = 3.

%t Table[Mod[n,Floor[1/2+Sqrt[2n]]],{n,100}] (* _Harvey P. Dale_, Feb 09 2013 *)

%o (Python)

%o from math import isqrt

%o def A088673(n): return n%((m:=isqrt(k:=n<<1))+(k>m*(m+1))) # _Chai Wah Wu_, Nov 07 2024

%Y Cf. A002024.

%K nonn,easy

%O 1,5

%A _Gary W. Adamson_, Oct 04 2003

%E Corrected and extended by _Ray Chandler_, Oct 04 2003

%E Corrected offset by _Chai Wah Wu_, Nov 07 2024