cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A306105 Numbers with digits in {0,1,2} such that every other digit is strictly less than its neighbors.

Original entry on oeis.org

0, 1, 2, 10, 20, 21, 101, 102, 201, 202, 212, 1010, 1020, 1021, 2010, 2020, 2021, 2120, 2121, 10101, 10102, 10201, 10202, 10212, 20101, 20102, 20201, 20202, 20212, 21201, 21202, 21212, 101010, 101020, 101021, 102010, 102020, 102021, 102120, 102121
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2018

Keywords

Comments

Terms of A032858 written in base 3.
There are A000045(n+2) terms with n digits (where 0 is taken to have no digits), so the first term with n digits is at index A000071(n+3). See A032858 for the proof.

Crossrefs

Cf. A306106 .. A306111 and A297147: analog for bases 3..9 and 10.
Cf. A000045 (Fibonacci), A000071(n) = Sum(k=0..n-2,A45(k)) = A000045(n)-1.
Cf. A032858 and A032859 .. A032865 for other bases 3..10.

Programs

  • PARI
    {A=[0,1,2]; F=[1,1]; for(n=0,4, F=[F[2],vecsum(F)]; for(k=1,3, T=max(k*10,21)*10^n; A=concat(A,apply(t->t+T,A[F[2]-1+if(k>2,F*[2,-1]~)..vecsum(F)-2]))));A}

Formula

a(n) = A007089(A032858(n)).

A032859 Numbers whose base-4 representation Sum_{i=0..m} d(i)*4^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 9, 12, 13, 14, 17, 18, 19, 33, 34, 35, 38, 39, 49, 50, 51, 54, 55, 59, 68, 72, 73, 76, 77, 78, 132, 136, 137, 140, 141, 142, 152, 153, 156, 157, 158, 196, 200, 201, 204, 205, 206, 216, 217, 220, 221, 222, 236, 237, 238
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A007090, A306106.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

Programs

  • Mathematica
    Join[{0},Select[Range[250],(Sign/@Differences[IntegerDigits[#,4]]) == PadRight[ {},IntegerLength[#,4]-1,{-1,1}]&]] (* Harvey P. Dale, Sep 18 2022 *)

Extensions

a(1)=0 inserted by Georg Fischer, Dec 18 2020

A032864 Numbers whose base-9 representation Sum_{i=0..m} d(i)*9^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 163, 164, 165, 166, 167, 168, 169, 170, 173
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A007095.
Different from A032888.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

Extensions

a(1)=0 inserted by Georg Fischer, Dec 18 2020

A032860 Numbers whose base-5 representation Sum_{i=0..m} d(i)*5^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 26, 27, 28, 29, 51, 52, 53, 54, 57, 58, 59, 76, 77, 78, 79, 82, 83, 84, 88, 89, 101, 102, 103, 104, 107, 108, 109, 113, 114, 119, 130, 135, 136, 140, 141, 142, 145, 146, 147, 148, 255
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A007091.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

Extensions

a(1)=0 inserted by Georg Fischer, Dec 18 2020

A032862 Numbers whose base-7 representation Sum_{i=0..m} d(i)*7^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 14, 15, 21, 22, 23, 28, 29, 30, 31, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 148, 149, 150, 151, 152, 153, 156, 157, 158, 159, 160, 164
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A007093.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

Extensions

a(1)=0 inserted by Georg Fischer, Dec 18 2020

A032861 Numbers whose base-6 representation Sum_{i=0..m} d(i)*6^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 73, 74, 75, 76, 77, 80, 81, 82, 83, 109, 110, 111, 112, 113, 116, 117, 118, 119, 123, 124, 125, 145, 146, 147, 148, 149, 152, 153, 154, 155
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A007092.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

Programs

  • Mathematica
    sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n,6]]]},s==PadRight[{}, Length[ s],{-1,1}]]; Select[Range[0,200],sdQ] (* Harvey P. Dale, Dec 15 2017 *)

Extensions

a(1)=0 inserted by Georg Fischer, Dec 18 2020
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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