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A232175 Least positive k such that n^3 + k^2 is a square, or 0 of there is no such k. 3
0, 1, 3, 6, 10, 3, 21, 8, 36, 15, 55, 6, 78, 35, 15, 48, 136, 27, 171, 10, 42, 99, 253, 10, 300, 143, 81, 42, 406, 15, 465, 64, 88, 255, 35, 63, 666, 323, 91, 3, 820, 21, 903, 55, 66, 483, 1081, 48, 1176, 125, 85, 39, 1378, 81, 165, 28, 76, 783, 1711, 15, 1830, 899, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers n such that a(n) = n*(n-1)/2  appear to be A000430.

n = 1 is the only number for which a(n) = 0. - T. D. Noe, Nov 21 2013

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from T. D. Noe).

StackExchange, The cube of integer can be written as the difference of two square.

MATHEMATICA

Join[{0}, Table[k = 1; While[! IntegerQ[Sqrt[n^3 + k^2]], k++]; k, {n, 2, 100}]] (* T. D. Noe, Nov 21 2013 *)

PROG

(Python)

import math

for n in range(77):

   n3 = n*n*n

   y=1

   for k in xrange(1, 10000001):

     sum = n3 + k*k

     r = int(math.sqrt(sum))

     if r*r == sum:

       print str(k)+', ',

       y=0

       break

   if y: print '-, ',

(Python)

from __future__ import division

from sympy import divisors

def A232175(n):

    n3 = n**3

    ds = divisors(n3)

    for i in range(len(ds)//2-1, -1, -1):

        x = ds[i]

        y = n3//x

        a, b = divmod(y-x, 2)

        if not b:

            return a

    return 0 # Chai Wah Wu, Sep 12 2017

(PARI) a(n) = {k = 1; while (!issquare(n^3+k^2), k++); k; } \\ Michel Marcus, Nov 20 2013

CROSSREFS

Cf. A000290, A000430, A000578, A038202, A055527, A232176.

Sequence in context: A194035 A194049 A120028 * A065234 A082184 A080817

Adjacent sequences:  A232172 A232173 A232174 * A232176 A232177 A232178

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Nov 19 2013

STATUS

approved

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)