

A084318


Iterate function described in A084317 if started at initial value n until reaching a fixed point.


10



0, 2, 3, 2, 5, 23, 7, 2, 3, 5, 11, 23, 13, 3, 1129, 2, 17, 23, 19, 5, 37, 211, 23, 23, 5, 3251, 3, 3, 29, 547, 31, 2, 311, 31397, 1129, 23, 37, 373, 313, 5, 41, 379, 43, 211, 1129, 223, 47, 23, 7, 5, 317, 3251, 53, 23, 773, 3, 1129, 229, 59, 547, 61, 31237, 37, 2, 1129, 2311
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OFFSET

1,2


COMMENTS

Conjecture: fixed point always exists.
Some initial values capriciously provide very large prime fixedpoints. This behavior is illustrated in A084319 for initial value n=91.
Unlike the related home primes A037274, the trajectory of numbers in this procedure is not strictly increasing. Of the 8770 numbers < 10000 that have trajectories (that is, that are neither 1 nor prime) 3727 decrease at least once before reaching 30 digits. A sequence with no decreases is twice as likely to not terminate before 30 digits (10.0%) as one that has at least one decrease (4.8%).  Christian N. K. Anderson, May 04 2013


LINKS

Table of n, a(n) for n=1..66.
Christian N. K. Anderson, Table of n, steps to reach a(n), and a(n) for numbers where a(n) has fewer than 30 digits; NA otherwise. Also includes trajectories, factors separated by s.


EXAMPLE

a(0)=0 since no prime factors to concatenate;
a[p^j]=p for p prime(powers);
n=95=519: fixedpoint list is {95,519,3173,19167,36389},
so a(95)=36389, a prime.


MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] conc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[FixedPoint[conc, w], {w, 1, 90}] Table[conc[w], {w, 1, 128}]


CROSSREFS

Cf. A084317, A084319.
Sequence in context: A086507 A133568 A120716 * A084317 A037279 A163591
Adjacent sequences: A084315 A084316 A084317 * A084319 A084320 A084321


KEYWORD

base,nonn


AUTHOR

Labos Elemer, Jun 16 2003


STATUS

approved



