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%I #6 Dec 07 2019 12:18:27
%S 0,1,2,9,12,107,109,120,244,337,381,407,565,592,937,1209,1224,1341,
%T 1717,2032,2402,3280,4957,5149,5265,5644,7065,7240,8181,8820,9712,
%U 10732,11901,15059,18300,19120,20436,22672,24516,25139,28044,28550,36145,38221,66201,72335,77100
%N Number n such that a2 - n^3 is a triangular number (A000217), where a2 is the least square above n^3.
%C The sequence of cubes begins: 0, 1, 8, 729, 1728, 1225043, 1295029, 1728000, 14526784, 38272753, 55306341, ...
%C The sequence of squares begins: 1, 4, 9, 784, 1764, 1225449, 1295044, 1729225, 14531344, 38278969, 55308969, ...
%C The sequence of roots of these squares begins: 1, 2, 3, 28, 42, 1107, 1138, 1315, 3812, 6187, 7437, 8211, 13430, 14404, 28682, ...
%o (Python)
%o def isqrt(a):
%o sr = 1L << (long.bit_length(long(a)) >> 1)
%o while a < sr*sr: sr>>=1
%o b = sr>>1
%o while b:
%o s = sr+b
%o if a >= s*s: sr = s
%o b>>=1
%o return sr
%o def isTriangular(a):
%o a+=a
%o sr = isqrt(a)
%o return (a==sr*(sr+1))
%o for n in range(77777):
%o n3 = n*n*n
%o a = isqrt(n3)+1
%o if isTriangular(a*a-n3): print str(n)+',',
%Y Cf. A000217, A000290, A000578, A233401.
%K nonn
%O 1,3
%A _Alex Ratushnyak_, Dec 09 2013
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