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.

User: Dominick Cancilla

Dominick Cancilla's wiki page.

Dominick Cancilla has authored 25 sequences. Here are the ten most recent ones:

A180408 Nonzero digits not used in n.

Original entry on oeis.org

123456789, 23456789, 13456789, 12456789, 12356789, 12346789, 12345789, 12345689, 12345679, 12345678, 23456789, 23456789, 3456789, 2456789, 2356789, 2346789, 2345789, 2345689, 2345679, 2345678, 13456789, 3456789, 13456789, 1456789, 1356789, 1346789, 1345789
Offset: 0

Views

Author

Dominick Cancilla, Sep 02 2010

Keywords

Examples

			a(13) = 123456789 without 1 and 3 = 2456789.
a(123456789) = 0 (by definition).

Programs

  • Mathematica
    newn[n_]:=FromDigits[Complement[Range[9],IntegerDigits[n]]]; Table[newn[i],{i,50}] (* Harvey P. Dale, Nov 21 2010 *)

Formula

a(n) = 123456789 after removing any digits that appear in n. If n uses all digits, then a(n) = 0.

Extensions

More terms from Harvey P. Dale, Nov 21 2010

A180410 Unique digits used in n in numerical order.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 12, 13, 14, 15, 16, 17, 18, 19, 2, 12, 2, 23, 24, 25, 26, 27, 28, 29, 3, 13, 23, 3, 34, 35, 36, 37, 38, 39, 4, 14, 24, 34, 4, 45, 46, 47, 48, 49, 5, 15, 25, 35, 45, 5, 56, 57, 58, 59, 6, 16, 26, 36, 46, 56, 6, 67, 68, 69, 7
Offset: 1

Views

Author

Dominick Cancilla, Sep 02 2010

Keywords

Comments

a(n) = A227362(n) - A151949(n). - Reinhard Zumkeller, Jul 09 2013

Examples

			a(93077) = 0379 = 379. Seven is only used once and the digits are sorted. The initial zero is not shown.

Links

Crossrefs

This is identical to A180409 with the zeros removed.

Programs

  • Haskell
    import Data.List (nub, sort)
a180410 = read . sort . nub . show :: Integer -> Integer
-- Reinhard Zumkeller, Jul 09 2013
  • Maple
    a:= n-> parse(cat(sort([{convert(n, base, 10)[]}[]])[])):
seq(a(n), n=1..70);  # Alois P. Heinz, Sep 21 2022

Formula

a(n) = 0123456789 after any digits not appearing in n are removed.

A180412 Lexicographically earliest increasing sequence of numbers with all odd digits alternating with numbers with all even digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 31, 40, 51, 60, 71, 80, 91, 200, 311, 400, 511, 600, 711, 800, 911, 2000, 3111, 4000, 5111, 6000, 7111, 8000, 9111, 20000, 31111, 40000, 51111, 60000, 71111, 80000, 91111, 200000, 311111, 400000, 511111, 600000, 711111, 800000, 911111, 2000000
Offset: 1

Views

Author

Dominick Cancilla, Sep 02 2010

Keywords

Examples

			11 is all odd digits. The next number in which all of the digits are even is 20. The next number in which all of the digits are odd is 31.

Links

Crossrefs

Cf. A014261, A014263.

Programs

  • Mathematica
    nxt[n_]:=Module[{fidn=First[IntegerDigits[n]],len=IntegerLength[n]},Which[fidn==9,2*10^len, EvenQ[ fidn], FromDigits[PadRight[{fidn+1},len,1]],OddQ[fidn],FromDigits[PadRight[ {fidn+ 1}, len,0]]]]; NestList[nxt,1,50] (* Harvey P. Dale, Nov 26 2013 *)

Extensions

Name edited by Michel Marcus, Apr 16 2023

A180409 Unique digits used in n in numerical order (with 0 last).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 2, 23, 24, 25, 26, 27, 28, 29, 30, 13, 23, 3, 34, 35, 36, 37, 38, 39, 40, 14, 24, 34, 4, 45, 46, 47, 48, 49, 50, 15, 25, 35, 45, 5, 56, 57, 58, 59, 60, 16, 26, 36, 46, 56, 6
Offset: 1

Views

Author

Dominick Cancilla, Sep 02 2010

Keywords

Examples

			a(93077) = 3790. Seven is only used once and the digits are sorted with zero last

Programs

  • Mathematica
    udno[n_]:=Module[{c=Union[IntegerDigits[n]]},FromDigits[If[First[c] == 0, RotateLeft[ c],c]]]; Array[udno,70] (* Harvey P. Dale, Dec 23 2015 *)

Formula

a(n) = 1234567890 after any digits not appearing in n are removed

A180103 Floor( 100*(n-1)/n ).

Original entry on oeis.org

50, 66, 75, 80, 83, 85, 87, 88, 90, 90, 91, 92, 92, 93, 93, 94, 94, 94, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98, 98
Offset: 2

Views

Author

Dominick Cancilla, Aug 09 2010

Keywords

Examples

			a(3)=66 because 2/3=66%

Crossrefs

Cf. A180104.

Formula

a(n)=98 for 50<=n<=99. a(n) = 99 for n>=100.

Extensions

First, arbitrarily defined term removed - R. J. Mathar, Aug 11 2010

A180104 Floor( 100*n/(n-1) ).

Original entry on oeis.org

200, 150, 133, 125, 120, 116, 114, 112, 111, 110, 109, 108, 107, 107, 106, 106, 105, 105, 105, 105, 104, 104, 104, 104, 104, 103, 103, 103, 103, 103, 103, 103, 103, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102
Offset: 2

Views

Author

Dominick Cancilla, Aug 09 2010

Keywords

Examples

			a(3)=150 because 3/2=150%

Crossrefs

Cf. A180103

Formula

a(n)=101 for 52<=n<=101. a(n) = 100 for n>101.

Extensions

Definition rewritten - R. J. Mathar, Aug 11 2010

A179935 Squares where the number of decimal digits is also a square.

Original entry on oeis.org

0, 1, 4, 9, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041
Offset: 1

Views

Author

Dominick Cancilla, Aug 02 2010

Keywords

Examples

			100180081 is a square (10009^2). The number of digits in 100180081 is 9, also a square (3^2).

Crossrefs

Cf. A217761.

Programs

  • PARI
    isok(n) = issquare(n) && issquare(length(Str(n))); \\ Michel Marcus, Aug 28 2013

A179933 n replaced by a list of the distinct positive integers that can be formed with the decimal digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 1, 11, 1, 2, 12, 21, 1, 3, 13, 31, 1, 4, 14, 41, 1, 5, 15, 51, 1, 6, 16, 61, 1, 7, 17, 71, 1, 8, 18, 81, 1, 9, 19, 91, 2, 20, 1, 2, 12, 21, 2, 22, 2, 3, 23, 32, 2, 4, 24, 42, 2, 5, 25, 52, 2, 6, 26, 62, 2, 7, 27, 72, 2, 8, 28, 82, 2, 9, 29, 92, 3, 30, 1, 3, 13
Offset: 1

Views

Author

Dominick Cancilla, Aug 02 2010

Keywords

Examples

			1 is replaced by 1 because 1 is the only number that can be formed with the digits in 1.
10 is replaced by 1, 10 because these are the only distinct, nonzero numbers that can be formed with the digits in 10 (0 is not nonzero; 01=1 so it is not distinct).
12 is replaced by 1, 2, 12, 21.

A179932 Number of distinct positive integers that can be formed with the decimal digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 3, 5, 10, 10
Offset: 1

Views

Author

Dominick Cancilla, Aug 02 2010

Keywords

Examples

			a(1) = 1 because there is only one number that can be formed with the digits in 1.
a(10) = 2 because the digits in 10 can be used to make 0, 1, 01, and 10, but only 1 and 10 are both nonzero and unique (obviously, 01=1).

Programs

  • Mathematica
    Table[Length[Union[FromDigits/@Flatten[Permutations/@Flatten[ Table[ Partition[ IntegerDigits[t],n,1],{n,IntegerLength[t]}],1],1]/.(0-> Nothing)]], {t,110}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2016 *)

A179955 Numbers whose sum of digits is 10 and which contain no 0 digits.

Original entry on oeis.org

19, 28, 37, 46, 55, 64, 73, 82, 91, 118, 127, 136, 145, 154, 163, 172, 181, 217, 226, 235, 244, 253, 262, 271, 316, 325, 334, 343, 352, 361, 415, 424, 433, 442, 451, 514, 523, 532, 541, 613, 622, 631, 712, 721, 811, 1117, 1126, 1135, 1144, 1153, 1162, 1171
Offset: 1

Views

Author

Dominick Cancilla, Aug 03 2010

Keywords

Comments

Subset of A052224.
Finite sequence. Highest member is 1111111111.
Contribution from Zak Seidov, Aug 06 2010, as corrected by D. S. McNeil: There are exactly 511 terms.

Examples

			19 is an element of the list because 1+9 = 10.
109 is not an element because it contains a 0.

Links

Crossrefs

Cf. A007953, A017173, A052224.

Programs

  • Maple
    with(combinat):
sort(select(y->y<>10, map(x->parse(cat(x[])), map(p->permute(p)[], partition(10)))))[]; # Alois P. Heinz, Sep 24 2013
  • Mathematica
    Reap[For[n=1; k=1, n <= 2*10^9, n++, id = IntegerDigits[n]; If[Total[id] == 10 && FreeQ[id, 0], Print["a(", k, ") = ", n]; Sow[n]; k++]]][[2, 1]] (* Jean-François Alcover, Jan 08 2016 *)
sd10Q[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&Total[idn]==10]; Select[Range[1200],sd10Q] (* Harvey P. Dale, Oct 17 2016 *)

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