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A232177 Least positive k such that triangular(n) + triangular(k) is a square. 3
1, 2, 1, 2, 3, 1, 5, 6, 7, 8, 9, 5, 2, 12, 13, 1, 15, 16, 17, 3, 5, 20, 2, 22, 23, 8, 4, 26, 12, 3, 29, 30, 1, 5, 33, 34, 4, 36, 37, 15, 6, 29, 22, 5, 43, 19, 45, 7, 15, 48, 6, 50, 11, 52, 8, 41, 22, 7, 57, 58, 59, 9, 26, 62, 8, 64, 19, 66, 10, 68, 5, 9, 71, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangular(k) = A000217(k) = k*(k+1)/2.

For n>1, a(n) <= n-1, because with k=n-1: triangular(n) + triangular(k) = n*(n+1)/2 + (n-1)*n/2 = n^2.

LINKS

Table of n, a(n) for n=0..73.

MATHEMATICA

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

PROG

(Python)

import math

for n in range(77):

  tn = n*(n+1)/2

  for k in xrange(1, n+9):

    sum = tn + k*(k+1)/2

    r = int(math.sqrt(sum))

    if r*r == sum:

      print str(k)+', ',

      break

CROSSREFS

Cf. A000217, A000290.

Cf. A082183 (least k>0 such that triangular(n) + triangular(k) is a triangular number).

Cf. A212614 (least k>1 such that triangular(n) * triangular(k) is a triangular number).

Cf. A232176 (least k>0 such that n^2 + triangular(k) is a square).

Cf. A232179 (least k>=0 such that n^2 + triangular(k) is a triangular number).

Cf. A101157 (least k>0 such that triangular(n) + k^2 is a triangular number).

Cf. A232178 (least k>=0 such that triangular(n) + k^2 is a square).

Sequence in context: A078032 A162453 A008313 * A111377 A014046 A243919

Adjacent sequences:  A232174 A232175 A232176 * A232178 A232179 A232180

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Nov 20 2013

STATUS

approved

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Last modified February 20 04:19 EST 2018. Contains 299358 sequences. (Running on oeis4.)