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A375753
a(n) is the difference between n*(n+1)/2 and the next smaller square of a prime.
4
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
3,1
LINKS
EXAMPLE
a(3) = A000217(3) - A001248(1) = 6 - 2^2 = 2,
a(4) = A000217(4) - A001248(2) = 10 - 3^2 = 1.
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hugo Pfoertner, Aug 26 2024
STATUS
approved