cp's OEIS Frontend

A355625 a(1) = 1; for n > 1, a(n) is the number of terms in the first n-1 terms of the sequence that share a 1-bit with n in their binary expansions.

%I A355625 #15 Jul 11 2022 08:35:06
%S A355625 1,0,1,0,2,1,4,0,3,2,6,2,6,7,11,0,6,9,13,6,13,13,18,6,11,17,21,16,21,
%T A355625 22,26,0,14,16,26,14,23,25,31,12,22,27,34,27,33,34,39,19,31,35,43,36,
%U A355625 44,44,49,36,42,48,52,47,52,53,57,0,29,32,48,30,48,48,57,25,41,46,56,47,57,58,65,34
%N A355625 a(1) = 1; for n > 1, a(n) is the number of terms in the first n-1 terms of the sequence that share a 1-bit with n in their binary expansions.
%C A355625 The indices where a(n) = 1 in the first 500000 terms are 1, 3, 6. It is likely no more exist although this is unknown. Many terms of the sequence are close to the line a(n) = n although only the first term is a possible fixed point. In the first 500000 terms the lowest values not to appear are 5, 8, 10, 15, 20, 24, 28. It is likely these and other numbers never appear although this is unknown. All terms for n > 1 where n is a power of 2 equal 0.
%H A355625 Scott R. Shannon, <a href="/A355625/b355625.txt">Table of n, a(n) for n = 1..10000</a>
%H A355625 Scott R. Shannon, <a href="/A355625/a355625.png">Image of the first 500000 terms</a>. The green line is y = n.
%e A355625 a(7) = 4 as the total number of terms in the first six terms that share a 1-bit with 7 in their binary expansions is four, namely 1, 1, 2, 1.
%o A355625 (Python)
%o A355625 from itertools import count, islice
%o A355625 def agen():
%o A355625     an, alst = 1, [1]
%o A355625     for n in count(2):
%o A355625         yield an
%o A355625         an = sum(1 for k in alst if k&n)
%o A355625         alst.append(an)
%o A355625 print(list(islice(agen(), 80))) # _Michael S. Branicky_, Jul 10 2022
%Y A355625 Cf. A355621, A030190, A129760, A353989, A352763, A354606.
%K A355625 nonn,base
%O A355625 1,5
%A A355625 _Scott R. Shannon_, Jul 10 2022