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A075246
y-value of the solution (x,y,z) to 4/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The x and z components are in A075245 and A075247.
14
4, 3, 4, 7, 15, 7, 10, 16, 34, 13, 18, 29, 61, 21, 30, 46, 96, 31, 43, 67, 139, 43, 60, 92, 190, 57, 78, 121, 249, 73, 100, 154, 316, 91, 124, 191, 391, 111, 154, 232, 474, 133, 181, 277, 565, 157, 99, 326, 664, 183, 248, 379, 771, 211, 286, 436, 886, 241, 326
OFFSET
3,1
COMMENTS
See A073101 for more details.
See A257840 for a variant that differs from a(89) on. - M. F. Hasler, Jul 03 2022
LINKS
MAPLE
A075246:=proc() local t, n, a, b, t1, largey, largez; for n from 3 to 100 do t:=4/n; largez:=0; largey:=0; for a from floor(1/t)+1 to floor(3/t) do t1:=t - 1/a; for b from max(a, floor(1/t1)+1) to floor(2/(t1)) do if and(type(1/(t1 - 1/b), integer), a<b, b<(1/(t1 - 1/b))) then if (1/(t1 - 1/b))>largez then largez:=(1/(t1 - 1/b)); largey:=b; end if end if end do; end do; lprint(n, largey) end do; end proc; # [program derived from A192787] Patrick J. McNab, Aug 20 2014
MATHEMATICA
For[xLst={}; yLst={}; zLst={}; n=3, n<=100, n++, cnt=0; xr=n/4; If[IntegerQ[xr], x=xr+1, x=Ceiling[xr]]; While[yr=1/(4/n-1/x); If[IntegerQ[yr], y=yr+1, y=Ceiling[yr]]; cnt==0&&y>x, While[zr=1/(4/n-1/x-1/y); cnt==0&&zr>y, If[IntegerQ[zr], z=zr; cnt++; AppendTo[xLst, x]; AppendTo[yLst, y]; AppendTo[zLst, z]]; y++ ]; x++ ]]; yLst
PROG
(PARI) apply( {A075246(n, c=1, a, t)=for(x=n\4+1, 3*n\4, for(y=max(1\t=4/n-1/x, x)+1, ceil(2/t)-1, t-1/y >= c && break; numerator(t-1/y)==1 && [c, a]=[t-1/y, y])); a}, [3..99]) \\ M. F. Hasler, Jul 03 2022
CROSSREFS
Cf. A073101 (number of solutions), A075245 (x values), A075247 (z values), A192787 (number of solutions with x <= y <= z), A257840 (variant: lex earliest solution, not largest z).
Sequence in context: A359864 A361849 A339409 * A257840 A132984 A277528
KEYWORD
hard,nice,nonn
AUTHOR
T. D. Noe, Sep 10 2002
STATUS
approved