A375752 - OEIS

%I #18 Sep 27 2024 16:33:26

%S 0,1,3,2,2,5,5,2,2,5,5,2,2,7,5,2,4,9,11,2,2,5,7,8,2,5,5,2,2,5,5,4,2,

%T 11,5,2,2,7,9,2,16,5,7,2,12,5,5,2,16,5,5,2,2,9,13,16,2,11,7,2,2,5,11,

%U 2,4,5,5,4,8,5,7,2,8,7,9,2,2,23,11,2,12,17,11,12,2

%N a(n) is the difference between T=n*(n+1)/2 and the largest prime not exceeding T.

%F a(n) = A000217(n) - A065384(n). - _Michel Marcus_, Aug 27 2024

%t Table[T=n(n+1)/2;T-If[PrimeQ[T],T,NextPrime[T,-1]],{n,2,86}] (* _James C. McMahon_, Sep 27 2024 *)

%o (PARI) a(n) = my(t=n*(n+1)/2); t - precprime(t)

%o (Python)

%o from sympy import prevprime

%o def A375752(n): return (t:=n*(n+1)//2) - prevprime(t) # _Karl-Heinz Hofmann_, Aug 27 2024

%Y Cf. A000217, A007917, A065384, A075402, A375753, A375754.

%K nonn,easy

%O 2,3

%A _Hugo Pfoertner_, Aug 26 2024