login
Lexicographically earliest sequence of positive terms such that for any distinct i and j, a(i) | a(j+1) <> a(j) | a(j+1) (where "|" corresponds to binary concatenation, A163621).
2

%I #14 Dec 18 2019 14:29:55

%S 1,1,2,1,3,2,2,3,3,4,1,4,2,4,3,5,2,5,3,6,1,8,1,9,2,8,2,9,3,7,4,4,5,4,

%T 8,3,8,4,9,4,10,2,11,2,13,1,10,4,11,3,9,5,8,5,9,6,4,15,2,16,1,16,2,17,

%U 2,18,4,16,3,10,5,10,6,5,11,4,17,3,11,5,14

%N Lexicographically earliest sequence of positive terms such that for any distinct i and j, a(i) | a(j+1) <> a(j) | a(j+1) (where "|" corresponds to binary concatenation, A163621).

%C This sequence is a binary variant of A318225.

%C This sequence has similarities with A088177; here we combine successive terms by concatenation, there by multiplication.

%C This sequence is necessarily unbounded.

%C Also, the value 1 appears infinitely many times.

%H Rémy Sigrist, <a href="/A330524/b330524.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms, alongside their binary representation and that of the concatenation of two consecutive terms, are:

%e n a(n) bin(a(n)) bin(a(n)|a(n+1))

%e -- ---- --------- ----------------

%e 1 1 1 11

%e 2 1 1 110

%e 3 2 10 101

%e 4 1 1 111

%e 5 3 11 1110

%e 6 2 10 1010

%e 7 2 10 1011

%e 8 3 11 1111

%e 9 3 11 11100

%e 10 4 100 1001

%e 11 1 1 1100

%e 12 4 100 10010

%o (PARI) s=0; v=1; for (n=1, 81, print1 (v", "); for (w=1, oo, if (!bittest(s, k=v*2^#binary(w)+w), s+=2^k; v=w; break)))

%Y See A330525 for the concatenation of consecutive terms.

%Y Cf. A088177, A163621, A318225.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Dec 17 2019