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

%I A375753 #14 Aug 31 2024 14:46:09
%S A375753 2,1,6,12,3,11,20,6,17,29,42,56,71,15,32,2,21,41,62,84,107,11,36,62,
%T A375753 17,45,74,104,135,167,32,66,101,137,174,212,251,291,20,62,105,29,74,
%U A375753 120,167,215,264,314,365,9,62,116,171,227,284,30,89,149,42,104,167,231,296,2
%N A375753 a(n) is the difference between n*(n+1)/2 and the next smaller square of a prime.
%H A375753 Karl-Heinz Hofmann, <a href="/A375753/b375753.txt">Table of n, a(n) for n = 3..10000</a>
%e A375753 a(3) = A000217(3) - A001248(1) = 6 - 2^2 = 2,
%e A375753 a(4) = A000217(4) - A001248(2) = 10 - 3^2 = 1.
%o A375753 (PARI) a375753(n) = my(t=n*(n+1)/2, s=sqrtint(t)); t-precprime(s)^2
%o A375753 (Python)
%o A375753 from sympy import prevprime, integer_nthroot
%o A375753 def A375753(n): return (t:=n*(n+1)//2) - prevprime(integer_nthroot(t,2)[0]+1)**2
%o A375753 # _Karl-Heinz Hofmann_, Aug 27 2024
%Y A375753 Cf. A000217, A001248, A375752, A375754.
%K A375753 nonn,easy
%O A375753 3,1
%A A375753 _Hugo Pfoertner_, Aug 26 2024