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

Author

Antti Karttunen, Jul 25 2023

Keywords

• nonn
• look

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

Crossrefs

Cf. A007283, A163511, A364258, A364293.

Programs

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 *)

Formula

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