A375753 a(n) is the difference between n*(n+1)/2 and the next smaller square of a prime.

2, 1, 6, 12, 3, 11, 20, 6, 17, 29, 42, 56, 71, 15, 32, 2, 21, 41, 62, 84, 107, 11, 36, 62, 17, 45, 74, 104, 135, 167, 32, 66, 101, 137, 174, 212, 251, 291, 20, 62, 105, 29, 74, 120, 167, 215, 264, 314, 365, 9, 62, 116, 171, 227, 284, 30, 89, 149, 42, 104, 167, 231, 296, 2

Offset: 3

Author

Hugo Pfoertner, Aug 26 2024

Keywords

• nonn
• easy

Examples

			a(3) = A000217(3) - A001248(1) = 6 - 2^2 = 2,
a(4) = A000217(4) - A001248(2) = 10 - 3^2 = 1.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000217, A001248, A375752, A375754.

Programs

PARI

a375753(n) = my(t=n*(n+1)/2, s=sqrtint(t)); t-precprime(s)^2

Python

from sympy import prevprime, integer_nthroot
def A375753(n): return (t:=n*(n+1)//2) - prevprime(integer_nthroot(t,2)[0]+1)**2
# Karl-Heinz Hofmann, Aug 27 2024