A195265 Trajectory of 20 under iteration of the map x -> A080670(x).

20, 225, 3252, 223271, 297699, 399233, 715623, 3263907, 32347303, 160720129, 1153139393, 72171972859, 736728093411, 3245576031137, 11295052366467, 310807934835791, 1789205424940407, 31745337977379983, 1122916740775279751, 7251536377635958081, 151243563319717018007

Offset: 1

Author

N. J. A. Sloane, Sep 14 2011, based on a posting to the Sequence Fans Mailing List by Alonso del Arte

Keywords

• nonn
• base

Comments

The table that I submitted for A195264 (see the second link here) is still actively maintained by me. That includes all unknown-outcome evolutions starting with numbers up to 10000. If you click in that table on the 'unknown' beside the number 20 it will give you the current state of the evolution of the number 20. There was a bottleneck at Alonso20(102) [= A195265(103); we're using offset zero for our evolutions] involving a 62-digit factor, cracked by "Mathew" in MersenneForum on August 13. Sean A. Irvine subsequently extended that to Alonso20(109). The unfactored composite in Alonso20(110) is 178 digits long. I maintain links to sorted lists of unfactored composites at the bottom of the table. If anyone can factor any of these composites, submit the factorization to factordb.com and I will (eventually) find it; a personal heads-up would of course be appreciated. - Hans Havermann, Oct 27 2013

Examples

			20 = 2^2*5 -> 225 = 3^2*5^2 -> 3252 = 2^2*3*271 -> 223271 ...
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..110
• Hans Havermann, Table of n, A195264(n) for n = 1..10000 (includes links to lengthy (>40) and unknown-outcome evolutions, and a list of unfactored composites in the unknowns' last step)
• N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

Crossrefs

Cf. A037274, A080670, A195264, A195266, A230305.

Programs

Maple

# See A195266

Mathematica

A080670[n_] := ToExpression@StringJoin[ToString/@Flatten[DeleteCases[FactorInteger[n], 1, -1]]]; NestWhileList[A080670, i = 1; 20, (PrintTemporary[{i++, #}]; ! PrimeQ[#]) &, 1, 40] (* Wouter Meeussen, Oct 27 2013 *)

Extensions

Alonso del Arte computed 40 terms, D. S. McNeil extended it to 66 terms, Sean A. Irvine to 70 terms, Hans Havermann (Oct 27 2013) to 110 terms.