A292316 Oblong numbers equidistant from two other oblong numbers.
6, 42, 56, 72, 156, 306, 342, 380, 420, 506, 650, 702, 756, 930, 1056, 1332, 1406, 1806, 1892, 1980, 2070, 2256, 2352, 2550, 2756, 2970, 3080, 3192, 3306, 3422, 3540, 3782, 3906, 4556, 4692, 5112, 5256, 5550, 5852, 6006, 6162, 6320, 6806, 7140, 7482, 7656, 8190, 8372, 8556, 8742
Offset: 1
Keywords
Examples
6 = 2*3 is an oblong number and equidistant from 12 = 3*4 and 0 = 0*1. 342 = 18*19 is oblong number and equidistant from 132 = 11*12 and 552 = 23*24 (552-342 = 210; 342-132 = 210).
Programs
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Mathematica
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 *)
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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)
Formula
a(n) = A292314(n)/3.
Comments