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

Author

J. H. Conway and N. J. A. Sloane, Dec 10 2007

Keywords

• nonn
• base

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

Crossrefs

Cf. A133500, A133501. For records see A135382, A135383.

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;