A322015 -id:A322015 - cp's OEIS frontend

A322017 a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, else if A003188(n+1) < A003188(n) then a(n) = n+1, otherwise a(n) = 0.

0, 0, 1, 0, 3, 4, 7, 0, 7, 8, 9, 12, 0, 12, 15, 0, 15, 16, 17, 0, 19, 20, 23, 24, 0, 24, 25, 28, 0, 28, 31, 0, 31, 32, 33, 0, 35, 36, 39, 0, 39, 40, 41, 44, 0, 44, 47, 48, 0, 48, 49, 0, 51, 52, 55, 56, 0, 56, 57, 60, 0, 60, 63, 0, 63, 64, 65, 0, 67, 68, 71, 0, 71, 72, 73, 76, 0, 76, 79, 0, 79, 80, 81, 0, 83, 84, 87, 88, 0, 88, 89

Offset: 0

Antti Karttunen, Nov 24 2018

nonn

For all n, A207901(a(n)) divides A207901(n), and similarly for A302033.

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A003188, A322015, A322016, A322018.

Cf. also A207901, A302033.

g[n_] := BitXor[n, Floor[n/2]]; a[n_] := If[n == 0, 0, If[g[n] > g[n-1],  n-1, If[g[n+1] < g[n], n+1, 0]]]; Array[a, 100, 0] (* Amiram Eldar, Dec 05 2018 *)

A003188(n) = bitxor(n, n>>1);
A322017(n) = if(0==n, 0, if(A003188(n)>A003188(n-1), n-1, if(A003188(1+n) < A003188(n), n+1, 0)));

A322016 a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, otherwise a(n) = 0.

Original entry on oeis.org

0, 0, 1, 0, 3, 4, 0, 0, 7, 8, 9, 0, 0, 12, 0, 0, 15, 16, 17, 0, 19, 20, 0, 0, 0, 24, 25, 0, 0, 28, 0, 0, 31, 32, 33, 0, 35, 36, 0, 0, 39, 40, 41, 0, 0, 44, 0, 0, 0, 48, 49, 0, 51, 52, 0, 0, 0, 56, 57, 0, 0, 60, 0, 0, 63, 64, 65, 0, 67, 68, 0, 0, 71, 72, 73, 0, 0, 76, 0, 0, 79, 80, 81, 0, 83, 84, 0, 0, 0, 88, 89, 0, 0, 92, 0, 0, 0, 96, 97

Offset: 0

Antti Karttunen, Nov 24 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A003188, A034947, A322015, A322017.

With[{nn = 98}, {0, 0}~Join~Most@ ReplacePart[ConstantArray[0, nn], Map[# -> # &, Position[Partition[Array[BitXor[#, Floor[#/2]] &, nn], 2, 1], ?(First@ # < Last@ # &), {1}, Heads -> False][[All, 1]] ]]] (* _Michael De Vlieger, Nov 25 2018 *)
Join[{0,0},With[{t=Partition[Table[BitXor[n,Floor[n/2]],{n,100}],2,1]},Flatten[ If[#[[1]]<#[[2]],Position[t,#],0]&/@t]]] (* Harvey P. Dale, Jan 28 2021 *)

A003188(n) = bitxor(n, n>>1);
A322016(n) = if(0==n,0,if(A003188(n)>A003188(n-1),n-1,0));

A322016(n) = if(!n,0,(((kronecker(-1,n)+1)/2)*(n-1)));

a(0) = 0; for n > 0, a(n) = (1/2)*(A034947(n)+1)*(n-1).

cp's OEIS Frontend

A322017 a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, else if A003188(n+1) < A003188(n) then a(n) = n+1, otherwise a(n) = 0.

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A322016 a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, otherwise a(n) = 0.

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