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A292316 Oblong numbers equidistant from a oblong numbers pair. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A176308 A103763 A191764

Adjacent sequences:  A292313 A292314 A292315 * A292317 A292318 A292319

KEYWORD

nonn

AUTHOR

Antonio Roldán, Sep 14 2017

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.