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 A233401 Numbers k such that k^3 - b2 is a triangular number (A000217), where b2 is the largest square less than k^3. 2
 1, 4, 8, 21, 37, 40, 56, 112, 113, 204, 280, 445, 481, 560, 688, 709, 1933, 1945, 3601, 3805, 3861, 4156, 4333, 4365, 7096, 8408, 8516, 11064, 12688, 13609, 13945, 16501, 17080, 18901, 21464, 23125, 27244, 27364, 28141, 45228, 45549, 58321, 60061, 66245, 70585, 78688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The cubes k^3 begin: 1, 64, 512, 9261, 50653, 64000, 175616, 1404928, ... The squares b2 begin: 0, 49, 484, 9216, 50625, 63504, 175561, 1404225, ... Their square roots are 0, 7, 22, 96, 225, 252, 419, 1185, 1201, 2913, 4685, 9387, ... LINKS PROG (Python) def isqrt(a): sr = 1L << (long.bit_length(long(a)) >> 1) while a < sr*sr: sr>>=1 b = sr>>1 while b: s = sr+b if a >= s*s: sr = s b>>=1 return sr def isTriangular(a): a+=a sr = isqrt(a) return (a==sr*(sr+1)) for n in range(1, 79999): n3 = n*n*n b = isqrt(n3) if b*b==n3: b-=1 if isTriangular(n3-b*b): print str(n)+', ', (PARI) f(k) = if (issquare(k), sqrtint(k-1)^2, sqrtint(k)^2); \\ adapted from A048760 isok(k) = my(b2 = sqrtint(k^3-1)^2); (k^3-b2) && ispolygonal(k^3-b2, 3); \\ Michel Marcus, Jan 26 2019 CROSSREFS Cf. A000217, A000290, A000578, A048760, A233400. Sequence in context: A308233 A037020 A094878 * A006908 A079860 A061256 Adjacent sequences: A233398 A233399 A233400 * A233402 A233403 A233404 KEYWORD nonn AUTHOR Alex Ratushnyak, Dec 09 2013 STATUS approved

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Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)