A375752 a(n) is the difference between T=n*(n+1)/2 and the largest prime not exceeding T.

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

Offset: 2

Author

Hugo Pfoertner, Aug 26 2024

Keywords

• nonn
• easy

Crossrefs

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

Programs

Mathematica

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

PARI

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

Python

from sympy import prevprime
def A375752(n): return (t:=n*(n+1)//2) - prevprime(t) # Karl-Heinz Hofmann, Aug 27 2024

Formula

a(n) = A000217(n) - A065384(n). - Michel Marcus, Aug 27 2024