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

Author

Antonio Roldán, Sep 14 2017

Keywords

• nonn

Comments

Oblong numbers (A002378) that are the arithmetic mean of two other oblong numbers. - R. J. Mathar, Oct 05 2017

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).
		

Crossrefs

Cf. A002378, A292309, A292310, A292313, A292314.

Programs

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 *)

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.