A261162 List run lengths of digits different from '2'. Lexicographically first such sequence of nonnegative numbers with no repeated terms.

1, 2, 0, 3, 22, 4, 5, 6, 20, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 30, 12, 31, 33, 32, 34, 35, 36, 23, 37, 38, 39, 40, 41, 43, 44, 45, 46, 42, 47, 48, 49, 52, 50, 51, 53, 54, 24, 55, 56, 57, 58, 25, 59, 60, 61, 63, 62, 64, 65, 66, 67, 68, 72, 69, 70, 71, 73, 74, 75, 82, 76, 77, 78, 79, 80, 81, 83, 26

Offset

1,2

Comments

In the concatenation of all terms of this sequence, "12032245620...", consider the digits '2' as delimiters of chunks of other digits, "1", "03", "", "456", .... The lengths of these chunks are given by the terms of the sequence. At any point, the next term is the smallest number not occurring earlier and not leading to a contradiction.

Links

Table of n, a(n) for n=1..81.

Eric Angelini, To reach the next "1", SeqFan list, August 10, 2015.

Example

The sequence starts with a(1) = 1 digits different from '2'. (It cannot start with a(1) = 0 since this would require to start with a chunk of 0 digits different from '2', i.e., with a digit '2': contradiction.)
Then, the first '2' which occurs as a(2) = 2, must be followed by a(2) = 2 digits different from '2', and the smallest possible choices are a(3) = 0 and a(4) = 3.
The following digit '2', first digit of a(5), must immediately be followed by another digit '2' (because of a(3) = 0), thus a(5) = 22. (Since 2 already occurred earlier, a(5) = 2 followed by a(6) = 20 is not possible. The choice a(4) = 12 would be possible but lead to a lexicographically larger sequence, since they are compared term-wise and not digit-wise.)
Then follow a(4) = 3 other digits before the next '2' in a(9), etc.

Prog

(PARI) A261162(n=99, d=2, a=1, p=0, u=[-1], r=u)={for(n=2, n, print1(a", "); p+=#digits(a)+!a; r=concat(r, r[#r]+a+1); while(#r>1&&r[1]<p, r=r[2..-1]); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[2..-1]); for(k=u[1]+1, 9e9, setsearch(u, k)&&next; if(r[1] >= p+#dk=if(k, digits(k), [0]), setsearch(Set(dk), d)&&next, for(i=1, #dk, (dk[i]==d)==!setsearch(r, p+i-1)&&next(2))); a=k; next(2)); error); a}

Crossrefs

Sequence in context: A135433 A223706 A347034 * A218862 A243199 A305212

Adjacent sequences: A261159 A261160 A261161 * A261163 A261164 A261165

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Aug 10 2015

Status

approved