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A233422 Numbers n such that m - n^3 is a square, where m is the least square above n^3. 1
0, 2, 3, 6, 12, 20, 24, 30, 40, 42, 56, 60, 68, 75, 78, 84, 87, 120, 126, 160, 180, 248, 264, 270, 273, 308, 312, 318, 330, 336, 351, 360, 396, 564, 570, 588, 615, 620, 630, 635, 720, 738, 780, 840, 912, 1008, 1016, 1032, 1284, 1308, 1320, 1334, 1344, 1404, 1540, 1617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that A070929(n) is a nonzero square.

The sequence of cubes a(n)^3 begins: 0, 8, 27, 216, 1728, 8000, 13824, 27000, 64000, 74088, 175616, 216000, 314432, ...

The sequence of m's begins: 1, 9, 36, 225, 1764, 8100, 13924, 27225, 64009, 74529, 176400, 216225, 314721, ...

The sequence of square roots of these m's begins: 1, 3, 6, 15, 42, 90, 118, 165, 253, 273, 420, 465, 561, 650, 689, 770, 812, ...

The sequence of squares m-n^3 begins: 1, 1, 9, 9, 36, 100, 100, 225, 9, 441, 784, 225, 289, 625, 169, 196, 841, ...

The sequence of their square roots begins: 1, 1, 3, 3, 6, 10, 10, 15, 3, 21, 28, 15, 17, 25, 13, 14, 29, 35, 43, 24, ... (note the first 12 terms are triangular numbers, A000217).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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 isSquare(a):

  sr = isqrt(a)

  return (a==sr*sr)

for n in xrange(77777):

  n3 = n*n*n

  a = isqrt(n3)+1

  if isSquare(a*a-n3):  print str(n)+', ',

(PARI) is(n)=issquare((sqrtint(n=n^3)+1)^2-n) \\ Charles R Greathouse IV, Dec 09 2013

CROSSREFS

Cf. A000290, A000578, A070929, A077115, A154101, A233400, A233401.

Sequence in context: A000423 A007335 A103070 * A079708 A096571 A227940

Adjacent sequences:  A233419 A233420 A233421 * A233423 A233424 A233425

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Dec 09 2013

STATUS

approved

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Last modified June 16 21:13 EDT 2019. Contains 324155 sequences. (Running on oeis4.)