A135381 -id:A135381 - cp's OEIS frontend

A135382 Records in A135381.

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, 5832000, 30840979456, 102372436321763328, 5385144351531158470656, 95883934811108205920256, 8384433103482628092198912000, 271349238454240747975480442880000, 194420753673323618666864443392000000000, 2230117087799166503951875964107867690793619500826624, 1262524163403573488849931050070387361916429306607697920000000

Offset: 1

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

For every term shown, the high point of the trajectory is the initial term.

			2230117087799166503951875964107867690793619500826624 = 2^94 * 3^43 * 7^3. The next term is 2^120 * 3^40 * 5^7.

Cf. A133500, A135381, A135383.

A135383 Where records occur in A135381.

Original entry on oeis.org

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, 25, 26, 35, 37, 39, 99, 473, 547, 593, 668, 2499, 64748

Offset: 1

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

Cf. A133500, A135381, A135382.

A133501 Number of steps for "powertrain" operation to converge when started at n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 2, 3, 3, 1, 1, 1, 3, 2, 5, 5, 5, 4, 9, 1, 1, 2, 5, 3, 3, 4, 6, 3, 5, 1, 1, 3, 2, 3, 5, 3, 3, 2, 4, 1, 1, 6, 3, 4, 4, 3, 3, 8, 2, 1, 1, 6, 6, 2, 2, 3, 5, 3, 2, 1, 1, 5, 3, 4, 4, 5, 4, 3, 7, 1, 1, 2, 5, 4, 2, 3, 3, 2, 4, 1, 1, 1, 1, 1

Offset: 0

J. H. Conway and N. J. A. Sloane, Dec 03 2007

See A133500 for definition.

It is conjectured that every number converges to a fixed-point.

			39 -> 19683 -> 1594323 -> 38443359375 -> 59440669655040 -> 0, so a(39) = 5.

N. J. A. Sloane, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Full trajectories of numbers from 1 to 10000

For the powertrain map itself, see A133500.

See A133508, A133503 for records. See A135381 for high-water marks.

powertrain:=proc(n) local a,i,n1,n2,t1,t2; n1:=abs(n); n2:=sign(n); t1:=convert(n1, base, 10); t2:=nops(t1); a:=1; for i from 0 to floor(t2/2)-1 do a := a*t1[t2-2*i]^t1[t2-2*i-1]; od: if t2 mod 2 = 1 then a:=a*t1[1]; fi; RETURN(n2*a); end;
# Compute trajectory of n under repeated application of the powertrain map of A133500. This will return -1 if the trajectory does not converge to a single number in 100 steps (so it could fail if the trajectory enters a nontrivial loop or takes longer than 100 steps to converge).
PTtrajectory := proc(n) local p,M,t1,t2,i; M:=100; p:=[n]; t1:=n; for i from 1 to M do t2:=powertrain(t1); if t2 = t1 then RETURN(n,i-1,p); fi; t1:=t2; p:=[op(p),t2]; od; RETURN(n,-1,p); end;

cp's OEIS Frontend

A135382 Records in A135381.

Views

Author

Keywords

Comments

Examples

Crossrefs

A135383 Where records occur in A135381.

Views

Author

Keywords

Crossrefs

A133501 Number of steps for "powertrain" operation to converge when started at n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple