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A233401
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Numbers k such that k^3 - b2 is a triangular number (A000217), where b2 is the largest square less than k^3.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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, ...
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LINKS
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Table of n, a(n) for n=1..46.
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PROG
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(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
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CROSSREFS
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Cf. A000217, A000290, A000578, A048760, A233400.
Sequence in context: A308233 A037020 A094878 * A006908 A079860 A061256
Adjacent sequences: A233398 A233399 A233400 * A233402 A233403 A233404
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KEYWORD
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nonn
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AUTHOR
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Alex Ratushnyak, Dec 09 2013
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STATUS
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approved
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