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

1,1

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.

Links

Table of n, a(n) for n=1..68.

Mathematica

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

Prog

(PARI) forcomposite(n=1, 1e6, A230625(n)<n&&print1(n", "))

Crossrefs

Cf. A230625, A195330, A080670, A287874.

Sequence in context: A070662 A350181 A183982 * A239523 A361821 A129820

Adjacent sequences: A287760 A287761 A287762 * A287764 A287765 A287766

Keyword

nonn,base

Author

M. F. Hasler, Jun 21 2017

Status

approved