cp's OEIS Frontend

A372644 For n >= 1, a(n) is the least k >= 1 such that for some x >= 1, n^2 - k^2 = x^3 or a(n) = -1 if no such k exists.

%I A372644 #14 May 12 2024 02:01:21
%S A372644 -1,-1,1,-1,-1,3,-1,-1,-1,6,-1,-1,-1,13,3,-1,15,-1,-1,-1,15,-1,-1,8,
%T A372644 -1,-1,-1,21,25,-1,-1,-1,-1,-1,15,28,-1,-1,-1,-1,-1,6,11,-1,36,-1,-1,
%U A372644 24,-1,-1,-1,-1,-1,-1,45,-1,39,-1,-1,15,-1,46,35,-1,-1,55
%N A372644 For n >= 1, a(n) is the least k >= 1 such that for some x >= 1, n^2 - k^2 = x^3 or a(n) = -1 if no such k exists.
%C A372644 For a given n this is a minimal solution of the Diophantine equation n^2 - k^2 = x^3 in positive integers. The solution exists only for n from A070745.
%e A372644 n = 3: 9 - k^2 = x^3 is true for k = 1 and x = 2, thus a(3) = 1.
%e A372644 n = 6: 36 - k^2 = x^3 is true for k = 3 and x = 3, thus a(6) = 3.
%o A372644 (Python)
%o A372644 from sympy import integer_nthroot
%o A372644 def A372644(n): return next((k for k in range(1,n) if integer_nthroot(n**2-k**2,3)[1]),-1) # _Chai Wah Wu_, May 11 2024
%Y A372644 Cf. A070745.
%K A372644 sign
%O A372644 1,6
%A A372644 _Ctibor O. Zizka_, May 08 2024