A239087 -id:A239087 - cp's OEIS frontend

A239083 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e < f, and S is always extended with the smallest integer not yet present in S.

1, 2, 10, 3, 11, 4, 12, 13, 14, 15, 5, 6, 16, 17, 7, 8, 18, 19, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 200, 201, 121, 122, 130, 202

Offset: 1

Michel Marcus and N. J. A. Sloane, Mar 10 2014

More than the usual number of terms are given in order to show that the pattern breaks after 120.
Computed by Lars Blomberg.
This is the first (Sa) of a family of 25 similar sequences. For others see
A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.
The sequence So (see link) has d > e = f in the definition. It does not have its own entry in the OEIS because it begins with the numbers 1 through 99. Using x-y to indicate the numbers from x through y, the sequence So begins like this:
1-99,101-109,120,110-112,121,201,113,122-130,114,131,202,132-140,115,141,
203,142-150,116,151,204,152-160,117,161,205,162-170,118,171,206, 172-180,
119,181,207,182-191, 208,192-199,209, 210,212-219,230, 220-223,231, 224,232,
301, 225,233-240,226,241,227,242, ...
Likewise, the sequence Sw is omitted for a similar reason. It has d = e > f in the definition, and begins 1-89,99,999,9999,99999,999999,9999999,..., continuing with strings of 9's.
Again, the sequences Sx and Sy are omitted because they are too close to A130571.
Sx (which has d = e >= f) begins
1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
61-66, 70,67-69,71-77,80,78,79,81-88,90,89,100,91-98,101,120,102-109,
112-119,121,122,300, 123-133,400,134-144,500,145-155,600,156-166,700,
167-177,800,178-188,900,189-198,200-202, ...
and Sy (d = e = f) begins
1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
61-66, 70,67-69,71-77,80,78,79,81-88,90,89,91-110,112-221,223-332,334-443,
445-554,556-665, 667-776,778-887,889-899,1001,900-989,1002,990-998,1003-1010,...
The sequences Sd, Si, Sl, Sq are omitted because they do not have enough terms to warrant their own entries.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Gleb Ivanov, Table of n, a(n) for n = 1..10000
Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sa)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author] (see sequence Sa)

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[s=Array[a,n-1],k]||Or@@(#<#2<#3&@@@Partition[Flatten[IntegerDigits/@Join[s[[-2;;]],{k}]],3,1]),k++];k];Array[a,126] (* Giorgos Kalogeropoulos, May 13 2022 *)

is_ok = lambda s: not any(s[i-2] < s[i-1] < s[i] for i in range(2, len(s)))
terms, appears, digits = [1],{1},'1'
for i in range(100):
    t = 1
    while not(t not in appears and is_ok(digits + str(t))):
        t += 1
    terms.append(t); appears.add(t); digits = digits + str(t)
    digits = digits[-2:]
print(terms) # Gleb Ivanov, Dec 04 2021

A239086 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e = f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 66, 68

Offset: 1

N. J. A. Sloane, Mar 10 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Se)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[s=Array[a,n-1],k]||Or@@(#<#2==#3&@@@Partition[Flatten[IntegerDigits/@Join[s[[-2;;]],{k}]],3,1]),k++];k];Array[a,68] (* Giorgos Kalogeropoulos, May 14 2022 *)

A239090 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e < f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111

Offset: 1

N. J. A. Sloane, Mar 11 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sp)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A239136 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e < f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 10, 3, 11, 101, 102, 12, 13, 14, 4, 15, 5, 16, 6, 17, 7, 18, 8, 19, 9, 20, 21, 22, 103, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 104, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 105, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 106, 56, 57, 58, 59, 60

Offset: 1

Michel Marcus, Mar 11 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sf)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A239139 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive decimal digits then we do not have d <= e = f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 20, 13, 14, 15, 16, 17, 18, 19, 21, 23, 22, 30, 24, 25, 26, 27, 28, 29, 31, 32, 34, 33, 40, 35, 36, 37, 38, 39, 41, 42, 43, 45, 44, 50, 46, 47, 48, 49, 51, 52, 53, 54, 56, 55, 60, 57, 58, 59, 61, 62, 63, 64, 65, 67, 66

Offset: 1

Michel Marcus, Mar 11 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sj)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A239215 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e > f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 999, 9999, 99999, 999999, 9999999, 99999999

Offset: 1

Michel Marcus, Mar 12 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sr)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[s=Array[a,n-1],k]||Or@@(#>=#2>#3&@@@Partition[Flatten[IntegerDigits/@Join[Last@s,{k}]],3,1]),k++];k];Array[a,56] (* Giorgos Kalogeropoulos, May 13 2022 *)

A239218 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d = e < f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 101, 20, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 102, 30, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 103, 40, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 104, 50, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 105, 60, 56, 57, 58, 59, 61

Offset: 1

Michel Marcus, Mar 12 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Su)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A239235 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d = e <= f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 101, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 102, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 103, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 104, 56, 57, 58, 59, 60, 61, 62, 63, 64

Offset: 1

Michel Marcus, Mar 13 2014

Computed by Lars Blomberg.

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sv)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A130571 Lexicographically earliest permutation of the natural numbers such that in decimal representation the final digit of each term is distinct from the initial digit of the succeeding term.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 30, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 40, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 50, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 60, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 70, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 80, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 90, 89, 100, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 200, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 201, 202, 112, 113, 114

Offset: 0

Reinhard Zumkeller, Jun 05 2007

More than the usual number of terms are displayed, in order to show the difference between this and some closely related sequences. - N. J. A. Sloane, Mar 13 2014
A010879(a(n)) <> A000030(a(n+1));
A130572 is the inverse permutation; A130573(n) = a(a(n));
a(A130575(n)) = A130575(n);
see A130576 and A130577 for record values and where they occur.

For a closely related family of sequences see A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

A239137 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e <= f, and S is always extended with the smallest integer not yet present in S.

Original entry on oeis.org

1, 2, 10, 3, 12, 13, 14, 15, 4, 5, 16, 17, 6, 7, 18, 19, 8, 9, 20, 21, 30, 31, 32, 40, 41, 42, 43, 22, 102, 103, 23, 24, 25, 26, 27, 28, 29, 33, 104, 34, 35, 36, 37, 38, 39, 44, 105, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73

Offset: 1

Michel Marcus, Mar 11 2014

Computed by Lars Blomberg.

Numbers a(n) = 0, 1, 11 (mod 100) cannot be added to this sequence, otherwise the sequence would terminate with 1, 2, 10, 3, 11. - Gleb Ivanov, Dec 06 2021

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013

Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sg)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author]

The sequences in this family are given in A239083-A239086, A239136-A239139, A239087-A239090, A239215-A239218, A239235.

is_ok = lambda s: not any(s[i-2] <= s[i-1] <= s[i] for i in range(2, len(s)))
terms, appears, digits = [1], {1}, '1'
for i in range(100):
    t = 1
    while not(
        t not in appears
        and is_ok(digits + str(t))
        and t % 100 not in [0, 1, 11]
    ): t += 1
    terms.append(t); appears.add(t); digits = digits + str(t)
    digits = digits[-2:]
print(terms) # Gleb Ivanov, Dec 06 2021

a(56) corrected by Gleb Ivanov, Dec 17 2021

cp's OEIS Frontend

A239083 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e < f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Python

A239086 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e = f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

A239090 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e < f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A239136 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e < f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A239139 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive decimal digits then we do not have d <= e = f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A239215 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e > f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

A239218 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d = e < f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A239235 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d = e <= f, and S is always extended with the smallest integer not yet present in S.

Views

Author

Keywords

Comments

References

Links

Crossrefs

A130571 Lexicographically earliest permutation of the natural numbers such that in decimal representation the final digit of each term is distinct from the initial digit of the succeeding term.

Views

Author

Keywords

Comments

Links

Crossrefs

A239137 The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e <= f, and S is always extended with the smallest integer not yet present in S.