cp's OEIS Frontend

A359663 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 terms of the Champernowne string starting from 1.

%I A359663 #7 Jan 10 2023 07:59:05
%S A359663 1,3,2,4,5,6,7,8,9,10,12,47,14,21,15,13,11,16,18,61,20,67,73,22,24,26,
%T A359663 25,28,30,17,27,32,33,107,109,36,19,29,34,38,127,39,35,137,40,42,44,
%U A359663 45,48,46,49,51,43,50,54,52,57,31,55,193,56,60,23,58,62,64,63,66,65,68,70,72,69,77,75,37
%N A359663 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 terms of the Champernowne string starting from 1.
%C A359663 For the Champernowne string starting from 1 see A033307. In the first 100000 terms there are 45 fixed points: 1, 4, 5, 6, 7, ..., 252, 264, 319. It is plausible no more exist. The sequence is conjectured to be a permutation of the positive integers.
%H A359663 Scott R. Shannon, <a href="/A359663/a359663.png">Image of the first 100000 terms</a>. The green line is a(n) = n.
%e A359663 a(3) = 2 as the sum of the first 3 terms of the Champernowne string is 1 + 2 + 3 = 6, and 2 is the smallest unused number that shares a factor with 6.
%e A359663 a(10) = 10 as the sum of the first 10 terms of the Champernowne string is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 = 46, and 10 is the smallest unused number that shares a factor with 46.
%Y A359663 Cf. A033307, A065648, A359114 (base-2), A027749.
%K A359663 nonn,base
%O A359663 1,2
%A A359663 _Scott R. Shannon_, Jan 10 2023