cp's OEIS Frontend

A230764 Length of chunks of even digits, delimited by an odd digit, in the concatenation of all terms; smallest such sequence without repeated terms.

%I A230764 #21 Dec 23 2024 14:53:43
%S A230764 1,2,3,4,6,5,8,20,7,22,24,21,26,28,9,40,42,44,23,46,48,60,62,64,66,68,
%T A230764 80,82,25,84,86,88,10,200,202,204,206,208,220,201,222,224,226,228,240,
%U A230764 242,244,203,246,248,260,262,264,266,205,268,280,282,284,286
%N A230764 Length of chunks of even digits, delimited by an odd digit, in the concatenation of all terms; smallest such sequence without repeated terms.
%C A230764 Cut the sequence of digits of the concatenation of all terms after each odd digit: 1|23|465|8207|222421|26289|40424423|46..., then the length of the segments is given by the sequence itself. This defines the sequence, with the additional requirements that no number can appear more than once, and that the smallest possible term must always be chosen.
%C A230764 There cannot be two odd digits in a row, which excludes many numbers such as 11, 13, 15, .... Moreover, after the initial terms, no "small" numbers with more than one odd digit can be present. Therefore this cannot be a permutation of the integers, and numbers with odd digit(s) (and, in particular, primes) become increasingly sparse.
%C A230764 See A230765 for the "dual" version where chunks of odd digits are delimited by an even digit.
%C A230764 See A230763 for a version where, instead of digits, the English spelling of the terms is considered.
%H A230764 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/011815.html">Cut the sequence after it's odd/even digits</a>, SeqFan List, Oct 29 2013
%o A230764 (PARI) A230764_vec(n, a=[], s=[],u=0)={my(check(a, s)=my(L=0, j=1); !for(i=1, #s, ( i>L+a[j] || (( i==L+a[j] )!= bittest(s[i],0))) && return; bittest(s[i],0) || next; L=i; j++)); check(a, s)||return; n-- || return(a); my(t); for(k=1, 9e9, bittest(u,k)&&next; (t=A230764_vec(n, concat(a, k), concat(s, digits(k)), u+2^k))&& return(t))}
%K A230764 nonn,base
%O A230764 1,2
%A A230764 _Eric Angelini_ and _M. F. Hasler_, Oct 29 2013