A233401 - OEIS

A233401

Numbers k such that k^3 - b2 is a triangular number (A000217), where b2 is the largest square less than k^3.

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

Table of n, a(n) for n=1..46.

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: A371001 A037020 A094878 * A006908 A079860 A061256

Adjacent sequences: A233398 A233399 A233400 * A233402 A233403 A233404

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Dec 09 2013

STATUS

approved