A287763 Numbers n for which A230625(n) < n, where A230625 is the concatenation of the prime factorization written in binary, converted back to decimal.

25, 27, 32, 49, 54, 64, 81, 96, 98, 121, 125, 128, 135, 147, 162, 169, 189, 192, 216, 224, 242, 243, 245, 250, 256, 289, 297, 320, 338, 343, 351, 352, 361, 363, 375, 384, 392, 405, 416, 432, 448, 486, 500, 507, 512, 513, 529, 539, 567, 576, 578, 605, 621, 625, 637, 640, 648, 675, 686, 704, 722, 729, 736, 750, 768, 775, 783, 784

Offset: 1

Author

M. F. Hasler, Jun 21 2017

Keywords

• nonn
• base

Comments

Relevant for the study of closed orbits. (This is to A230625 the analog of A195330 for A080670.) Up to a certain limit, the trajectory of all numbers, under iteration of A230625, end either in a prime (fixed point) or in one of the orbits {1007, 1269} or {1503,3751}.

See A288985 for the analog when A287874 is used instead of A230625, i.e., without converting back the concatenation of the binary strings to decimal, or rather, reading it as a decimal number.

Crossrefs

Cf. A230625, A195330, A080670, A287874.

Programs

Mathematica

Select[Range@ 800, Function[n, FromDigits[#, 2] < n &@ Flatten@ Map[IntegerDigits[#, 2] &, FactorInteger[n] /. {p_, 1} :> {p}]]] (* Michael De Vlieger, Jun 23 2017 *)

PARI

forcomposite(n=1,1e6,A230625(n)