A376242 a(n) = least m >= 0 such that (x = f(A376241(n)), y = f(m), z = (x+y)/(xy-1)) yields an integer x+y+z = x*y*z, where f(m) = A002487(m)/A002487(m+1).

0, 1, 2, 1, 6, 2, 2, 14, 4, 30, 12, 35, 2, 4, 9, 20, 4, 8, 126, 56, 32, 152, 52, 254, 61, 84, 40, 16, 4, 510, 368, 320, 212, 48, 396, 72, 583, 1022, 792, 368, 98, 188, 340, 80, 583, 339, 140, 32, 233, 2046, 480, 384, 583, 2062, 852, 188, 328

Offset: 1

Author

M. F. Hasler, Sep 16 2024

Keywords

• nonn

Comments

A376241 uses the Stern-Brocot sequence s = A002487 to enumerate all (nonnegative) rational x = s(n)/s(n+1) and similarly y = s(m)/s(m+1), WLOG m <= n, which yield an integer x*y*z = x+y+z with (necessarily) z = (x+y)/(xy-1). The present sequence lists the m-values corresponding to the n-values listed in A376241.

Examples

			The terms correspond to the following solutions, with y = A002487(m)/A002487(m+1):
   m |  x  |  y  |  z  | xyz = x+y+z
-----+-----+-----+-----+------------
   0 |  0  |  0  |  0  |   0
   1 |  2  |  1  |  3  |   6
   2 | 3/2 | 1/2 | -8  |  -6
   1 |  3  |  1  |  2  |   6
   6 | 4/3 | 2/3 | -18 |  -16
   2 | 5/2 | 1/2 |  12 |   15
   2 |  4  | 1/2 | 9/2 |   9
  14 | 5/4 | 3/4 | -32 |  -30
  ...| ... | ... | ... |  ...
		

Crossrefs

Cf. A002487 (Stern-Brocot sequence), A376241 (corresponding n values), A376243 (set of absolute values of corresponding xyz = x+y+z).

Programs

PARI

A376242(n, k=A376241(n))={my(p, q=1, x=A002487(k)/A002487(k+1)); for(m=2, k, my(y=(p=q)/q=A002487(m)); x*y != 1 && denominator(x+y+(x+y)/(x*y-1))==1 && return(m-1))} \\ Short of a function A376241(n), one can simply provide a term k = A376241(n) as second argument and omit the first argument n.