A098670 -id:A098670 - cp's OEIS frontend

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

Paolo P. Lava, Mar 26 2012

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

			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.

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

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.

#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

Edited by M. F. Hasler, Oct 10 2013

A098645 List the positions of all digits '1' in the sequence. This is the lexicographically earliest increasing sequence with this property.

Original entry on oeis.org

1, 3, 10, 20, 22, 31, 32, 33, 34, 35, 41, 51, 52, 53, 54, 55, 111, 112, 200, 210, 220, 222, 231, 1111, 2000, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2020, 2022, 2023, 2024, 2031, 10000, 20000, 20002, 20003, 20004, 20005, 20006, 20007, 20008, 20009

Offset: 1

Eric Angelini, Oct 27 2004

Start with a(1) = 1. For n > 1, choose a(n) to be the smallest number > a(n-1) consistent with the condition that "the a(n)-th digit is a 1 and no 1's occur in other positions" is true for all n.
If we change "> a(n-1)" to "not already used", we get 1, 3, 10, 6, 11, 7, 21, 13, 15, 17, 19, 101, ... - David Wasserman, Feb 26 2008
That sequence has by now been entered as A210415. - M. F. Hasler, Oct 08 2013

			The first digit of the sequence is a "1", the 3rd digit also, then the 10th, the 11th, etc.

Index to the OEIS: Entries related to self-referencing sequences.

Cf. A098670. See A114134 for another version. See also A210414-A210423.

Entry revised by Eric Angelini and N. J. A. Sloane, Feb 03 2006.

More terms from David Wasserman, Feb 26 2008

A210416 List the positions of all digits 2 in the concatenation of all terms, not necessarily in order. This is the lexicographically earliest such sequence.

Original entry on oeis.org

2, 20, 1, 6, 21, 9, 22, 10, 15, 23, 19, 222, 220, 25, 27, 29, 32, 35, 200, 40, 201, 45, 202, 47, 52, 203, 51, 59, 204, 64, 205, 69, 206, 74, 207, 79, 208, 84, 209, 89, 210, 94, 211, 99, 212, 101, 108, 213, 114, 214, 120, 215, 118, 127, 132, 216, 131, 141, 217

Offset: 1

Paolo P. Lava, Mar 26 2012

See A210415 for comments, links, and code.

See A098670 for a variant with increasing terms. - M. F. Hasler, Oct 08 2013

			The sequence starts with 2: the second digit is equal to 2. In the second position we cannot write only 2 because the first number is already 2. So we use the minimum number greater than 2 and beginning with digit 2, i.e., 20. In the third position we can write 1 because the digit in the first position is 2. And so on.

Danny Rorabaugh, Table of n, a(n) for n = 1..1000

Cf. A098670, A210414-A210423.

A114134 Start with a(1) = 1. For n>1, choose a(n) to be the smallest number > a(n-1) consistent with the condition that "the a(n)-th digit is a 1" is true for all n.

Original entry on oeis.org

1, 3, 10, 11, 12, 21, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 1111, 11111, 111111, 1111111, 11111111, 11111112, 11111113

Offset: 1

Eric Angelini, Oct 27 2004

There can be 1's in other positions too.

Sequence A098645 does not allow 1's in other positions, A210415 is a variant which does not impose a(n)>a(n-1). - M. F. Hasler, Oct 08 2013

			The first digit of the sequence is a "1", the 3rd digit also, then the 10th, the 11th, etc.

Index to the OEIS: Entries related to self-referencing sequences.

Cf. A098670. See A098645 for another version.

Cf. A210414-A210423.

Entry revised by Eric Angelini and N. J. A. Sloane, Feb 03 2006.

More terms from Rick L. Shepherd, Feb 05 2006

cp's OEIS Frontend

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.

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A098645 List the positions of all digits '1' in the sequence. This is the lexicographically earliest increasing sequence with this property.

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A210416 List the positions of all digits 2 in the concatenation of all terms, not necessarily in order. This is the lexicographically earliest such sequence.

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A114134 Start with a(1) = 1. For n>1, choose a(n) to be the smallest number > a(n-1) consistent with the condition that "the a(n)-th digit is a 1" is true for all n.

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