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Least k>1 such that triangular(n) + triangular(n+k) is a square.
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%I #8 Apr 01 2014 10:25:33

%S 8,4,10,16,22,6,34,40,14,52,58,8,16,76,82,24,94,100,106,10,23,124,20,

%T 136,142,25,36,160,22,12,178,184,55,46,202,208,54,220,226,34,56,14,26,

%U 31,262,36,274,66,49,89,28,304,65,316,76,16,48,84,346,352,358,86,50,376

%N Least k>1 such that triangular(n) + triangular(n+k) is a square.

%C For n>0, a(n) <= 6*n-2 because triangular(n) + triangular(7*n-2) = (5*n-1)^2.

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

%o s=[]; for(n=0, 100, k=2; while(!issquare(triangular(n)+triangular(n+k)), k++); s=concat(s, k)); s \\ _Colin Barker_, Mar 31 2014

%Y Cf. A000217, A232177.

%K nonn

%O 0,1

%A _Alex Ratushnyak_, Mar 30 2014