OFFSET
3,1
COMMENTS
In other words, smallest solution k>0 to 4*k^2 + 8*(k + 1)*n + 8*n^2 + 4*k + 1 = m^2. - Ralf Stephan, Apr 01 2014
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 3..1000
EXAMPLE
a(3) = 2 because triangular(3)+triangular(3+2)=21 is a triangular number.
a(5) = 1 because triangular(5)+triangular(5+1)=36 is a triangular number.
In other words, k=a(3)=2 is the smallest positive solution to 4*k^2 + 28*k + 97 = m^2, and k=a(5)=1 is the smallest positive solution to 4*k^2 + 44*k + 241 = m^2.
PROG
(PARI) triangular(n) = n*(n+1)/2;
is_triangular(n) = issquare(8*n+1);
s=[]; for(n=3, 100, k=1; while(!is_triangular(triangular(n)+triangular(n+k)), k++); s=concat(s, k)); s \\ Colin Barker, Mar 31 2014
(Haskell)
a239969 n = head [k | k <- [1..],
a010054 (a000217 n + a000217 (n + k)) == 1]
-- Reinhard Zumkeller, Apr 03 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Mar 30 2014
EXTENSIONS
First PROG corrected by Colin Barker, Apr 04 2014
STATUS
approved