A357148 - OEIS

%I #16 Sep 16 2022 23:45:19

%S 1,3,5,7,9,15,16,15,16,24,29,32,33,29,34,29,32,36,34,42,61,64,34,32,

%T 61,64,61,64,61,64,65,72,76,64,72,85,76,64,72,82,64,72,100,104,100,91,

%U 64,72,64,72,104,100,116,127,128,129,133,128,129,128,129,128,129

%N a(n) = A357082(n-1) + A357082(n).

%H Scott R. Shannon, <a href="/A357148/b357148.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="https://oeis.org/A357082/a357082_5.png">Bitmap of (a(n-1) + a(n))</a>, n = 1..2^11, 12X vertical exaggeration, read horizontally where black represents 1 and white 0, with least significant bit on bottom.

%H Michael De Vlieger, Let sequence b list primitive terms in this sequence. <a href="/A357148/a357148.png">Annotated plot a(n) = b(k) at (n, k)</a> for n = 1..84.

%H Michael De Vlieger, <a href="/A357148/a357148_1.png">Plot a(n) = b(k) at (n, k)</a> for n = 1..2^12.

%H Scott R. Shannon, <a href="/A357148/a357148_2.png">Image for n = 0..2250000</a>.

%t nn = 120; c[_] = False; j = a[0] = 0; u = 1; w = "0"; Do[k = u; While[Or[c[k], StringContainsQ[w, Set[v, IntegerString[j + k, 2]]]], k++]; Set[{a[n], c[k], b[n]}, {k, True, j + k}]; Set[{j, w}, {k, w <> IntegerString[k, 2]}]; If[k == u, While[c[u], u++]], {n, nn}], n]; Array[b, nn] (* _Michael De Vlieger_, Sep 15 2022 *)

%o (Python)

%o from itertools import islice

%o def agen():

%o     aset, astr, an, mink = {0}, "0", 0, 1

%o     while True:

%o         k = mink

%o         while k in aset or bin(an+k)[2:] in astr: k += 1

%o         while mink in aset: mink += 1

%o         yield an+k; an = k; aset.add(an); astr += bin(an)[2:]

%o print(list(islice(agen(), 63))) # _Michael S. Branicky_, Sep 16 2022

%Y Cf. A357082.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Sep 15 2022