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.
%I A106840 #9 Sep 14 2024 06:50:34
%S A106840 1,4,8,9,16,17,20,25,32,33,36,40,41,49,52,57,64,65,68,72,73,80,81,84,
%T A106840 89,97,100,104,105,113,116,121,128,129,132,136,137,144,145,148,153,
%U A106840 160,161,164,168,169,177,180,185,193,196,200,201,208,209,212,217,225
%N A106840 Numbers m such that both m and m+1 have odd part of the form 4*k+1.
%C A106840 From _Amiram Eldar_, Sep 14 2024: (Start)
%C A106840 Disjoint union of A017077 and {4*A091072(n)}.
%C A106840 The asymptotic density of this sequence is 1/4. (End)
%H A106840 Amiram Eldar, <a href="/A106840/b106840.txt">Table of n, a(n) for n = 1..10000</a>
%e A106840 20/4 = 5 == 1 (mod 4) and also 21 == 1 (mod 4), therefore 20 is in the sequence.
%t A106840 f[n_] := Mod[n / 2^IntegerExponent[n, 2] - 1, 4]; SequencePosition[Array[f, 250], {0, 0}][[;;,1]] (* _Amiram Eldar_, Sep 14 2024 *)
%Y A106840 Cf. A017077, A091072, A106841, A106837.
%Y A106840 Contains A106841 and A106841+1.
%K A106840 nonn
%O A106840 1,2
%A A106840 _Ralf Stephan_, May 03 2005