cp's OEIS Frontend

A317922 a(n) = number of k with 0 < 2*k < n-1 such that a(n-k) AND a(n-2*k) = a(n-k) (where AND denotes the bitwise AND operator).

%I A317922 #12 May 10 2019 18:10:05
%S A317922 0,0,1,0,1,1,3,0,2,1,2,1,3,3,4,0,3,2,4,2,4,3,5,1,3,3,7,2,4,4,7,0,4,3,
%T A317922 6,5,7,4,8,2,6,4,12,1,10,5,7,2,7,1,9,3,5,6,9,4,7,3,7,3,11,5,8,3,8,4,
%U A317922 10,3,11,6,11,1,9,4,11,8,10,8,13,2,11,7,15
%N A317922 a(n) = number of k with 0 < 2*k < n-1 such that a(n-k) AND a(n-2*k) = a(n-k) (where AND denotes the bitwise AND operator).
%C A317922 This sequence has similarities with A317420.
%H A317922 Rémy Sigrist, <a href="/A317922/b317922.txt">Table of n, a(n) for n = 1..50000</a>
%H A317922 Rémy Sigrist, <a href="/A317922/a317922.png">Scatterplot of the first 10000000 terms</a>
%H A317922 Rémy Sigrist, <a href="/A317922/a317922_1.png">Colored scatterplot of the first 10000000 terms</a> (where the color is function of the 2-adic valuation of n (A001511))
%H A317922 Rémy Sigrist, <a href="/A317922/a317922_2.png">Colored scatterplot of the first 10000000 terms</a> (where the color is function of A000265(n) mod 16)
%H A317922 Rémy Sigrist, <a href="/A317922/a317922.txt">C++ program for A317922</a>
%e A317922 For n = 5:
%e A317922 - a(5-1) AND a(5-2) = 0 AND 1 = 0 = a(5-1),
%e A317922 - a(5-2) AND a(5-4) = 1 AND 0 = 0 <> a(5-2),
%e A317922 - hence a(5) = 1.
%o A317922 (C++) See Links section.
%Y A317922 Cf. A000265, A001511, A317420.
%K A317922 nonn,base
%O A317922 1,7
%A A317922 _Rémy Sigrist_, Aug 11 2018