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%I #15 Mar 24 2022 16:32:33
%S 6,42,56,72,156,306,342,380,420,506,650,702,756,930,1056,1332,1406,
%T 1806,1892,1980,2070,2256,2352,2550,2756,2970,3080,3192,3306,3422,
%U 3540,3782,3906,4556,4692,5112,5256,5550,5852,6006,6162,6320,6806,7140,7482,7656,8190,8372,8556,8742
%N Oblong numbers equidistant from two other oblong numbers.
%C Oblong numbers (A002378) that are the arithmetic mean of two other oblong numbers. - _R. J. Mathar_, Oct 05 2017
%F a(n) = A292314(n)/3.
%e 6 = 2*3 is an oblong number and equidistant from 12 = 3*4 and 0 = 0*1.
%e 342 = 18*19 is oblong number and equidistant from 132 = 11*12 and 552 = 23*24 (552-342 = 210; 342-132 = 210).
%t o[n_] := n(n+1); s[x_] := Reduce[ x+k == o[y] && x-k == o[z] && k>0 && z>0, {z, y, k}, Integers]; Select[o@ Range@ 93, s[#] =!= False &] (* _Giovanni Resta_, Sep 18 2017 *)
%o (PARI) t=2;k=2;while(t<=10^4,i=k;e=0;v=t+i;while(i>2&&e==0,if(issquare(4*v+1),e=1;print1(t,", "));i+=-2;v+=i);k+=2;t+=k)
%Y Cf. A002378, A292309, A292310, A292313, A292314.
%K nonn
%O 1,1
%A _Antonio Roldán_, Sep 14 2017
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