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.

A031999 Numbers whose base-4 digits are in nonincreasing order.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 16, 20, 21, 32, 36, 37, 40, 41, 42, 48, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 80, 84, 85, 128, 144, 148, 149, 160, 164, 165, 168, 169, 170, 192, 208, 212, 213, 224, 228, 229, 232, 233, 234, 240
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Identical to A023760 apart from its first term. - Charles R Greathouse IV, May 03 2016

Links

Crossrefs

Cf. A007090, A023760, A023786 (subset).

Programs

  • Mathematica
    Select[Range[300], Max[Differences[IntegerDigits[#, 4]]] < 1 &] (* Harvey P. Dale, Apr 27 2017 *)

A023786 Katadromes: digits in base 4 are in strict descending order.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 9, 12, 13, 14, 36, 52, 56, 57, 228
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

No more terms are possible because, although infinitely many numbers have base 4 digits in descending order, like 256, none beyond 228 can have them in strictly descending order. - Alonso del Arte, Feb 08 2019

Examples

			228 in base 4 is 3210. Since those digits are in strictly descending order, 228 is in the sequence.
229 in base 4 is 3211. Although those digits are in descending order, the repeated digit 1 means 229 is not in the sequence.

Crossrefs

Cf. A023760, A031999.

Programs

  • Mathematica
    Select[Range[0, 255], Max[Differences[IntegerDigits[#, 4]]] < 0 &] (* Harvey P. Dale, Dec 15 2014 *)

A272615 Numbers with digits in descending numerical order in base 2, 3 and 4 expansions.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 12, 63, 240
Offset: 1

Views

Author

Robin Powell, May 03 2016

Keywords

Comments

a(10), if it exists, has more than 1000 decimal digits. Conjecture: there are no more terms in this sequence. - Charles R Greathouse IV, May 03 2016

Examples

			12 is 1100 in base 2, 110 in base 3 and 30 in base 4; in each representation every digit is smaller than or equal to the one proceeding so 12 is a term.
Similarly, 63 is 111111 in base 2, 2100 in base 3 and 333 in base 4 so it is also a term.

Crossrefs

Intersection of A023758, A023759, and A023760.

Programs

  • PARI
    dec(n,b)=my(v=digits(n,b)); v==vecsort(v,,4)
is(n)=dec(n,2) && dec(n,3) && dec(n,4) \\ Charles R Greathouse IV, May 03 2016
  • PARI
    dec(n,b)=my(v=digits(n,b)); v==vecsort(v,,4)
list(lim)=my(v=List([0]),t); for(i=1,logint(lim\1+1,4), t=4^i-1; while(t<=lim, if(dec(t,3), listput(v,t)); t*=4); t=2*4^i-2; while(t<=lim, if(dec(t,3), listput(v,t)); t*=4)); Set(v) \\ Charles R Greathouse IV, May 03 2016
Showing 1-3 of 3 results.

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

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