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

2,3

Links

Table of n, a(n) for n=2..86.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A282161 A205675 A342331 * A058608 A112196 A021035

Adjacent sequences: A375749 A375750 A375751 * A375753 A375754 A375755

Keyword

nonn,easy

Author

Hugo Pfoertner, Aug 26 2024

Status

approved