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A239970 Least positive k such that triangular(k) + triangular(n+k) is a triangular number (A000217). 2
2, 5, 3, 6, 9, 4, 15, 18, 21, 5, 27, 30, 9, 36, 6, 42, 10, 48, 51, 14, 7, 60, 63, 15, 69, 72, 19, 8, 81, 26, 20, 13, 17, 24, 99, 9, 105, 14, 111, 114, 29, 120, 123, 126, 10, 132, 135, 34, 20, 144, 147, 35, 153, 45, 11, 29, 165, 33, 17, 174, 30, 44, 183, 186, 189, 12, 18, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) <= 3*n-3, because triangular(3*n-3) + triangular(4*n-3) = triangular(5*n-4).

In other words, smallest k>0 such that 8*k^2 + 4*(2*k + 1)*n + 4*n^2 + 8*k + 1 = m^2 has an integer solution. - Ralf Stephan, Apr 01 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

EXAMPLE

n=5: the smallest solution k>0 to 8*k^2 + 64*k + 225 = m^2 is k=4, so a(5)=4.

PROG

(PARI) triangular(n) = n*(n+1)/2;

is_triangular(n) = issquare(8*n+1);

s=[]; for(n=0, 100, k=1; while(!is_triangular(triangular(k)+triangular(n+k)), k++); s=concat(s, k)); s \\ Colin Barker, Mar 31 2014

(PARI) a(n)=my(k=1); while(!ispolygonal(k*(k+n+1)+(n^2+n)/2, 3), k++); k \\ Charles R Greathouse IV, Apr 01 2014

(Haskell)

a239970 n = head [k | k <- [1..],

                      a010054 (a000217 k + a000217 (n + k)) == 1]

-- Reinhard Zumkeller, Apr 03 2014

CROSSREFS

Cf. A000217, A239969.

Cf. A010054.

Sequence in context: A222072 A246007 A256997 * A111202 A194280 A163362

Adjacent sequences:  A239967 A239968 A239969 * A239971 A239972 A239973

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Mar 30 2014

EXTENSIONS

First PROG corrected by Colin Barker, Apr 04 2014

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)