cp's OEIS Frontend

A359114 a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n bits of the binary Champernowne string starting from 1.

%I A359114 #9 Jan 10 2023 07:59:23
%S A359114 1,2,4,3,6,5,10,15,8,9,7,12,18,21,14,11,16,13,26,39,52,20,22,24,25,28,
%T A359114 30,17,34,27,32,19,35,33,36,38,40,23,42,44,45,46,48,49,50,29,51,31,54,
%U A359114 55,57,60,63,66,56,58,62,64,65,68,69,70,37,74,72,76,78,75,80,41,82,77,81,84,43,86
%N A359114 a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n bits of the binary Champernowne string starting from 1.
%C A359114 For the binary Champernowne string starting from 1 see A030302. In the first 100000 terms the fixed points are 1, 2, 12, 24, 25; it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.
%H A359114 Scott R. Shannon, <a href="/A359114/a359114.png">Image of the first 100000 terms</a>. The green line is a(n) = n.
%e A359114 a(3) = 4 as the sum of the first 3 bits of the binary Champernowne string is 1 + 1 + 0 = 2, and 4 is the smallest unused number that shares a factor with 2.
%e A359114 a(10) = 9 as the sum of the first 10 bits of the binary Champernowne string is 1 + 1 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 0 = 6, and 9 is the smallest unused number that shares a factor with 6.
%Y A359114 Cf. A030302, A030303, A359663 (base-10), A027749.
%K A359114 nonn,base
%O A359114 1,2
%A A359114 _Scott R. Shannon_, Dec 16 2022