A210415 List the positions of all digits 1 in the concatenation of all terms, not necessarily in order. This is the lexicographically earliest such sequence.

1, 3, 10, 6, 11, 7, 21, 13, 15, 17, 19, 101, 24, 100, 29, 102, 34, 103, 39, 104, 44, 105, 49, 106, 54, 107, 59, 108, 64, 109, 69, 110, 70, 76, 111, 77, 78, 85, 112, 86, 91, 94, 113, 95, 211, 1111, 11111, 1110, 115, 116, 118, 119, 121, 122, 124, 125, 127, 129

Offset: 1

Author

Paolo P. Lava, Mar 26 2012

Keywords

• nonn
• base
• nice

Comments

Original name: "A self-describing sequence: The a(n) say the positions of the digits 1 inside the sequence when it is read as a string of digits."

For each n, the digit in position a(n) is equal to 1. At each step, choose the minimum integer not yet present in the sequence and not leading to a contradiction.

This sequence had been mentioned by Wasserman in 2008, cf. A098645, a variant of this sequence with additional restriction a(n+1) > a(n). - M. F. Hasler, Oct 08 2013

Examples

			The sequence starts with 1: the first digit is equal to 1. In the second position we cannot write 2 because the second digit would not be 1 but 2. Then we write 3. The third digit must be 1 and the minimum number starting with 1 is 10. And so on.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..1000
• Index to the OEIS: Entries related to self-referencing sequences.

Crossrefs

This construction for other decimal digits is A210414, A210416, A210417, A210418, A210419, A210420, A210421, A210422, A210423.

Variants of this sequence include A098645, A098670, A114134, A167519.

Programs

Sage

#Returns the first n terms of this sequence for digit d
def dig_loc(d,n):
  L, S = [], ""
  while len(L)lenS or S[new-1]==str(d) ) and ( (new-lenS-1 not in range(ext)) or a[new-lenS-1]==str(d) ) and ( d!=0 or lenS+ext+1!=new ):
          L.append(new)
          S += str(new)
          break
        else: new = 0
  return L
dig_loc(1,58) # Danny Rorabaugh, Nov 27 2015

Extensions

Edited by M. F. Hasler, Oct 10 2013