A239970 Least positive k such that triangular(k) + triangular(n+k) is a triangular number (A000217).
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
Offset: 0
Keywords
Examples
n=5: the smallest solution k>0 to 8*k^2 + 64*k + 225 = m^2 is k=4, so a(5)=4.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Programs
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Haskell
a239970 n = head [k | k <- [1..], a010054 (a000217 k + a000217 (n + k)) == 1] -- Reinhard Zumkeller, Apr 03 2014 -
Mathematica
tr[n_]:=(n(n+1))/2;lpk[n_]:=Module[{k=1},While[!OddQ[Sqrt[8(tr[k]+tr[n+k])+1]],k++];k]; Array[lpk,70,0] (* Harvey P. Dale, Nov 11 2024 *) -
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
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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
Extensions
First PROG corrected by Colin Barker, Apr 04 2014
Comments