A364294 Difference k - A163511(k) computed for those odd numbers k for which the difference is nonnegative.

0, 2, 8, 8, 20, 4, 28, 50, 28, 22, 58, 86, 110, 2, 52, 50, 128, 132, 166, 202, 236, 22, 124, 232, 136, 286, 146, 74, 246, 370, 352, 412, 452, 488, 238, 458, 216, 568, 362, 692, 68, 236, 338, 606, 754, 550, 536, 728, 854, 846, 904, 952, 994, 694, 478, 1124, 744, 1368, 96, 484, 1084, 1490, 10, 236, 812, 746, 1254

Offset

1,2

Comments

Conjecture: a(1) is the only zero in this sequence, which is equal to the claim that A007283 gives all fixed points of the map n -> A163511(n).

Question: What can be said about the occurrence of small values later in the sequence? Does the sequence admit any lower bound that is monotonic, and keeps on growing, thus never setting to any constant value? See the scatter plot.

Links

Antti Karttunen, Table of n, a(n) for n = 1..15157

Formula

a(n) = -A364258(A364293(n)).

Mathematica

f[n_] := Reverse@ Map[Ceiling[(Length@ # - 1)/2] &, DeleteCases[Split@ Join[Riffle[IntegerDigits[n, 2], 0], {0}], {k__} /; k == 1]]; Subtract @@ # & /@ Select[Array[{2 # - 1, Function[t, Prime[t] Product[Prime[m]^(f[2 # - 1][[m]]), {m, t}]][DigitCount[2 # - 1, 2, 1]]} &, 1024], #1 >= #2 & @@ # &] (* Michael De Vlieger, Jul 25 2023 *)

Crossrefs

Cf. A007283, A163511, A364258, A364293.

Sequence in context: A269510 A093907 A116471 * A146749 A250313 A180825

Adjacent sequences: A364291 A364292 A364293 * A364295 A364296 A364297

Keyword

nonn,look

Author

Antti Karttunen, Jul 25 2023

Status

approved