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 1-8 of 8 results.

A214488 List of words over {1,3} with equal numbers of 1's and 3's.

Original entry on oeis.org

13, 31, 1133, 1313, 1331, 3113, 3131, 3311, 111333, 113133, 113313, 113331, 131133, 131313, 131331, 133113, 133131, 133311, 311133, 311313, 311331, 313113, 313131, 313311, 331113, 331131, 331311, 333111
Offset: 1

Views

Author

Jonathan Vos Post, Jul 18 2012

Keywords

Comments

This is to 3 as A214218 is to 2. The subsequence of primes (when interpreted as decimal integers) is A087511.

Links

Crossrefs

Cf. A214218.

Programs

  • Maple
    sort([seq(seq((10^(2*d)-1)/9+2*add(10^i, i=s), s=combinat:-choose([$0..(2*d-1)], d)), d=1..4)]); # Robert Israel, Jul 09 2018
  • Mathematica
    Flatten[Table[Sort[FromDigits/@Permutations[PadRight[{},2n,{1,3}]]], {n,3}]] (* Harvey P. Dale, Aug 03 2014 *)

A111066 Numbers with digits 1 and 2 and at least one of each.

Original entry on oeis.org

12, 21, 112, 121, 122, 211, 212, 221, 1112, 1121, 1122, 1211, 1212, 1221, 1222, 2111, 2112, 2121, 2122, 2211, 2212, 2221, 11112, 11121, 11122, 11211, 11212, 11221, 11222, 12111, 12112, 12121, 12122, 12211, 12212, 12221, 12222, 21111, 21112, 21121, 21122, 21211
Offset: 1

Views

Author

Alexandre Wajnberg & Youri Mora, Oct 08 2005

Keywords

Links

Crossrefs

Equals A007931 minus A000042 and A002276. Supersequence of A214218.
Cf. A043494, A037415, A062289, A000225.

Programs

  • Mathematica
    FromDigits /@ Select[ IntegerDigits[ Range[210], 3], Union[ # ] == {1, 2} &] (* Robert G. Wilson v, Oct 09 2005 *)
Union[FromDigits/@Select[Flatten[Table[Tuples[{1,2},n],{n,2,5}],1], Union[#] == {1,2}&]] (* Harvey P. Dale, Sep 05 2013 *)
  • Python
    from itertools import count, islice
def agen():
    for i in count(1):
        s = bin(i+1)[3:].replace('1', '2').replace('0', '1')
        if 0 < s.count('1') < len(s):
            yield int(s)
print(list(islice(agen(), 42))) # Michael S. Branicky, Dec 21 2021

Extensions

More terms from Robert G. Wilson v, Oct 09 2005
Crossrefs from Charles R Greathouse IV, Aug 03 2010

A214521 List of words over {1,4} with equal numbers of 1's and 4's.

Original entry on oeis.org

14, 41, 1144, 1414, 1441, 4114, 4141, 4411, 111444, 114144, 114414, 114441, 141144, 141414, 141441, 144114, 144141, 144411, 411144, 411414, 411441, 414114, 414141, 414411, 441114, 441141, 441411, 444111, 11114444, 11141444
Offset: 1

Views

Author

Jonathan Vos Post, Jul 19 2012

Keywords

Comments

This is to 4 as A214488 is to 3, and as A214218 is to 2. The subsequence of primes (when interpreted as decimal integers) is A087512.

Crossrefs

Cf. A214218, A214488.

Programs

  • Mathematica
    Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,4}]],{n,4}],1]] (* Harvey P. Dale, Aug 30 2016 *)

A214522 List of words over {1,5} with equal numbers of 1's and 5's.

Original entry on oeis.org

15, 51, 1155, 1515, 1551, 5115, 5151, 5511, 111555, 115155, 115515, 115551, 151155, 151515, 151551, 155115, 155151, 155511, 511155, 511515, 511551, 515115, 515151, 515511, 551115, 551151, 551511, 555111
Offset: 1

Views

Author

Jonathan Vos Post, Jul 19 2012

Keywords

Comments

This is to 5 as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2. All of these, interpreted as decimal integers are divisible by 3, because each pair of "1" and "5" contributes a digital sum of 6, hence the total is divisible by 3.
The subsequence of semiprimes begins 15, 51, 15151551, 51115551, 51515511, 51555111, 55515111, 1115155551, 1115515551, 1151551551,..

Crossrefs

Cf. A214218, A214488, A214521.

Programs

  • Mathematica
    Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,5}]],{n,3}],1]] (* Harvey P. Dale, Aug 30 2016 *)

A214524 List of words over {1,6} with equal numbers of 1's and 6's.

Original entry on oeis.org

16, 61, 1166, 1616, 1661, 6116, 6161, 6611, 111666, 116166, 116616, 116661, 161166, 161616, 161661, 166116, 166161, 166611, 611166, 611616, 611661, 616116, 616161, 616611, 661116, 661161, 661611, 666111
Offset: 1

Views

Author

Jonathan Vos Post, Jul 19 2012

Keywords

Comments

This is to 6 as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2. The subsequence of primes (when interpreted as decimal integers) is A087513.

Links

Crossrefs

Cf. A214218, A214488, A214521, A214522.

Programs

  • Mathematica
    Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,6}]],{n,3}],1]] (* Harvey P. Dale, May 11 2015 *)

A214530 List of words over {1,7} with equal numbers of 1's and 7's.

Original entry on oeis.org

17, 71, 1177, 1717, 1771, 7117, 7171, 7711, 111777, 117177, 117717, 117771, 171177, 171717, 171771, 177117, 177171, 177711, 711177, 711717, 711771, 717117, 717171, 717711, 771117, 771171, 771711, 777111
Offset: 1

Views

Author

Jonathan Vos Post, Jul 20 2012

Keywords

Comments

This is to 7 as A214524 is to 6, as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2. The subsequence of primes (when interpreted as decimal integers) is A087514.

Crossrefs

Cf. A214218, A214488, A214521, A214522, A214524.

Programs

  • Mathematica
    Sort[FromDigits/@Flatten[Table[Permutations[PadRight[{},2n,{1,7}]],{n,3}],1]] (* Harvey P. Dale, Aug 30 2016 *)

A214531 List of words over {1,8} with equal numbers of 1's and 8's.

Original entry on oeis.org

18, 81, 1188, 1818, 1881, 8118, 8181, 8811, 111888, 118188, 118818, 118881, 181188, 181818, 181881, 188118, 188181, 188811, 811188, 811818, 811881, 818118, 818181, 818811, 881118, 881181, 881811, 888111
Offset: 1

Views

Author

Jonathan Vos Post, Jul 20 2012

Keywords

Comments

This is to 8 as A214530 is to 7, as A214530 is to 6, as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2. All of these, interpreted as decimal integers are divisible by 9, because each pair of "1" and "8" contributes a digital sum of 9, hence the total is divisible by 9.

Links

Crossrefs

Cf. A214218, A214488, A214521, A214522, A214524, A214530.

Programs

  • Mathematica
    With[{tb=Table[Join[PadRight[{},n,1],PadRight[{},n,8]],{n,3}]},FromDigits/@ Flatten[Permutations/@tb,1]] (* Harvey P. Dale, Jan 17 2014 *)

A214532 List of words over {1,9} with equal numbers of 1's and 9's.

Original entry on oeis.org

19, 91, 1199, 1919, 1991, 9119, 9191, 9911, 111999, 119199, 119919, 119991, 191199, 191919, 191991, 199119, 199191, 199911, 911199, 911919, 911991, 919119, 919191, 919911, 991119, 991191, 991911, 999111, 11119999, 11191999
Offset: 1

Views

Author

Jonathan Vos Post, Jul 20 2012

Keywords

Comments

This is to 9 as A214531 is to 8, as A214530 is to 7, as A214530 is to 6, as A214522 is to 5, as A214521 is to 4, as A214488 is to 3, and as A214218 is to 2.
The subsequence of primes (when interpreted as decimal integers) is A087515.

Crossrefs

Cf. A214218, A214488, A214521, A214522, A214524, A214530, A214531.

Programs

  • Mathematica
    FromDigits/@(Flatten[Permutations/@Table[Join[Table[1,{n}],Table[9,{n}]],{n,4}],1]) (* Harvey P. Dale, Aug 20 2014 *)
Showing 1-8 of 8 results.

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