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 1-4 of 4 results.

A032865 Numbers whose base-10 representation Sum_{i=0..m} d(i)*10^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, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Every other digit must be strictly less than its neighbor(s). - M. F. Hasler, Oct 05 2018

Links

Crossrefs

Cf. A032858 .. A032864 for base-3 .. 9 variants.

Programs

  • Mathematica
    sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n, 10]]]}, s==PadRight[{}, Length[s], {-1, 1}]]; Select[Range[0, 700], sdQ] (* Vincenzo Librandi, Oct 06 2018 *)
  • PARI
    is(n)=!for(i=2,#n=digits(n),(n[i-1]-n[i])*(-1)^i>0||return) \\ M. F. Hasler, Oct 05 2018

Extensions

Name corrected and cross-references and a(1) = 0 prepended by M. F. Hasler, Oct 05 2018

A306111 Numbers with digits in {0,...,8} such that every other digit is strictly less than its neighbors.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 101, 102, 103, 104, 105, 106, 107, 108, 201, 202, 203, 204, 205, 206, 207, 208, 212, 213, 214, 215, 216, 217, 218, 301, 302, 303, 304, 305, 306, 307
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2018

Keywords

Comments

Terms of A032864 written in base 9.

Examples

			There are 1+2+3+4+5+6+7+8 = 9*4 = 36 terms with 2 digits.
We obtain the 3-digit terms by appending to each of these the 1-digit terms starting with a digit larger than the last digit of the prefix: 10.{1..8}, 20.{1..8}, 21.{2..8}, 30.{1..8}, ..., 86.{7..8}, 87.{8}.
We obtain the 4-digit terms by appending to each of the 2 digit terms, the 2-digit terms starting with a digit larger than the last digit of the prefix: 10.{10,...,87}, 20.{10,...,87}, 21.{20,...,87}, 30.{10,...,87}, ..., 86.{70,...,87}, 87.{80..87}.
That way we obtain all terms with n digits by taking the 2-digit terms and appending to each of these the suitable subsequence of n-2 digit terms.

Crossrefs

Cf. A306105 .. A306110 and A297147: analog for bases 3..8 and 10.
Cf. A032864 and A032858 .. A032865 for other bases 3..10.

Programs

  • PARI
    A(Nmax=100,K=8,A=[0..K],i=vector(2*K,i,max(1,i-K+1)),c(T,v)=apply(t->t+T,v))={for(n=0,oo, for(k=10,K*11-1,if(k%10

Formula

a(n) = A007095(A032864(n)).
Numbers in A297147 having no digit 9: Intersection of A297147 with A007095.

A032863 Numbers whose base-8 representation Sum_{i=0..m} d(i)*8^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 16, 17, 24, 25, 26, 32, 33, 34, 35, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 193, 194, 195
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Base-8 digits must be strictly alternating in size: every other digit must be strictly less than its neighbor(s). Also: numbers whose base-8 expansion, considered as a decimal number, is in A032865 = the base-10 variant of this sequence. - M. F. Hasler, Oct 05 2018

Examples

			From _M. F. Hasler_, Oct 05 2018: (Start)
The base-8 representation of 7, 8, 16, 17, 24, 25, 26, 32, 33 is 7, 10, 20, 21, 30, 31, 32, 40, 41.
Numbers 61, 62, 65, 66, ..., 70, 71, 129, 130, ... have the base-8 expansion 76, 77, 101, 102, ..., 106, 107, 201, 202, ... (End)

Crossrefs

Cf. A032858, A032859, A032860, A032861, A032862, this sequence, A032864, A032865 for bases 3 to 10.

Programs

  • Mathematica
     sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n, 8]]]}, s==PadRight[{}, Length[s], {-1, 1}]]; Select[Range[0, 700], sdQ] (* Vincenzo Librandi, Oct 06 2018 *)
  • PARI
    is(n)=!for(i=2,#n=digits(n,8),(n[i-1]-n[i])*(-1)^i>0||return) \\ M. F. Hasler, Oct 05 2018

Extensions

a(1) = 0 added by Vincenzo Librandi, Oct 06 2018

A032888 Numbers whose base-9 representation Sum_{i=0..m} d(i)*9^i has d(0) < d(1) > d(2) < ...

Original entry on oeis.org

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, 99, 100, 108, 109, 110, 117, 118, 119, 120, 126, 127, 128, 129, 130, 135
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Different from A032864.
Showing 1-4 of 4 results.

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