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

1,1

Comments

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

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = A292314(n)/3.

Example

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).

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 *)

Prog

(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)

Crossrefs

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

Sequence in context: A186885 A097253 A083938 * A329000 A329339 A176308

Adjacent sequences: A292313 A292314 A292315 * A292317 A292318 A292319

Keyword

nonn

Author

Antonio Roldán, Sep 14 2017

Status

approved