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 1-3 of 3 results.

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

A306108 Numbers with digits in {0,...,5} such that every other digit is strictly less than its neighbors.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 101, 102, 103, 104, 105, 201, 202, 203, 204, 205, 212, 213, 214, 215, 301, 302, 303, 304, 305, 312, 313, 314, 315, 323, 324, 325, 401, 402, 403, 404, 405, 412, 413, 414, 415, 423, 424, 425, 434, 435, 501, 502, 503, 504, 505, 512, 513, 514
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2018

Keywords

Comments

Terms of A032861 written in base 6.

Crossrefs

Cf. A306105 .. A306111 and A297147: analog for bases 3..9 and 10.
Cf. A032862 and A032858 .. A032865 for other bases 3..10.

Programs

  • PARI
    A(Nmax=100, K=5, 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, if(k%10

Formula

a(n) = A007092(A032861(n)).

A306109 Numbers with digits in {0,...,6} such that every other digit is strictly less than its neighbors.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 101, 102, 103, 104, 105, 106, 201, 202, 203, 204, 205, 206, 212, 213, 214, 215, 216, 301, 302, 303, 304, 305, 306, 312, 313, 314, 315, 316, 323, 324, 325, 326, 401, 402, 403, 404, 405, 406, 412, 413, 414, 415
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2018

Keywords

Comments

Terms of A032862 written in base 7.

Crossrefs

Cf. A306105 .. A306111 and A297147: analog for bases 3..9 and 10.
Cf. A032863 and A032858 .. A032865 for other bases 3..10.

Programs

  • PARI
    A(Nmax=100, K=6, 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, if(k%10

Formula

a(n) = A007093(A032862(n)).
Showing 1-3 of 3 results.

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

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