A084323 Fixed points reached when prime-factor-concatenation function [A084317] is started at n!.

0, 2, 23, 23, 547, 547, 2357, 2357, 2357, 2357, 4359293547691, 4359293547691, 325798243129564339, 325798243129564339, 325798243129564339, 325798243129564339, 3947306373286437248759663633906484193454376823

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

a(n)=A084318[A000142(n)]=A084318[n! ]

Example

n=11: 11!=256.81.25.7.11; a(11)=iter[concatenate[{2,3,5,7,11}]] =A084318[39916800]; the list of iteration:
{39916800, 235711, 7151223, 34495309, 41841349, 1116722777, 1958774883, 313113444469, 744730492067, 4359293547691}
at each step the ordered prime factors of previous term are concatenated.

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] coc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[FixedPoint[coc, q[w]], {w, 1, 7}]

Crossrefs

Cf. A001405, A084317, A084318, A084322.

Sequence in context: A153656 A242037 A233692 * A131983 A153718 A105813

Adjacent sequences: A084320 A084321 A084322 * A084324 A084325 A084326

Keyword

base,nonn

Author

Labos Elemer, Jun 20 2003

Status

approved