A135381 a(n) = high point in trajectory of n under repeated application of powertrain map (see A133500).
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 32, 531441, 128, 256, 512, 30, 31, 32, 128, 81, 5832000, 729, 30840979456, 191102976, 102372436321763328, 40, 41, 42, 531441, 256, 1024, 531441, 531441, 5832000, 8470728, 50, 51, 32, 125, 625
Offset: 0
Examples
The trajectory of 39 is 39 -> 19683 -> 5038848 -> 214990848 -> 17179869184 -> 1735247072139264 -> 19999187712 -> 102372436321763328 -> 8813365017182208 -> 0, so a(39) = 102372436321763328.
Links
- N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Programs
-
Maple
maxtraj := proc(n) local h,p,M,t1,t2,i; M:=100; t1:=n; h:=n; for i from 1 to M do t2:=powertrain(t1); if t2 = t1 then RETURN(n,h); fi; if t2 > t1 then h:=t2; fi; t1:=t2; od; RETURN(n,-1); end;