cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A364294 #22 Jul 26 2023 14:33:16
%S A364294 0,2,8,8,20,4,28,50,28,22,58,86,110,2,52,50,128,132,166,202,236,22,
%T A364294 124,232,136,286,146,74,246,370,352,412,452,488,238,458,216,568,362,
%U A364294 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
%N A364294 Difference k - A163511(k) computed for those odd numbers k for which the difference is nonnegative.
%C A364294 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).
%C A364294 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.
%H A364294 Antti Karttunen, <a href="/A364294/b364294.txt">Table of n, a(n) for n = 1..15157</a>
%F A364294 a(n) = -A364258(A364293(n)).
%t A364294 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 *)
%Y A364294 Cf. A007283, A163511, A364258, A364293.
%K A364294 nonn,look
%O A364294 1,2
%A A364294 _Antti Karttunen_, Jul 25 2023