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 1-9 of 9 results.

A154871 Numbers n such that n^6 contains every digit exactly 4 times.

Original entry on oeis.org

3470187, 3554463, 3887058, 4328241, 4497738
Offset: 1

Views

Author

Zhining Yang, Jan 16 2009

Keywords

Comments

a(1) is also the number of A074205

Examples

			3887058^6=3449261536602702380309782557611971988544, which contains 4 times of each digit 0-9. Total 5 terms

Crossrefs

A054038 A074205 A154532 A154566 A154818

A154873 Numbers n such that n^5 contains every digit exactly 3 times.

Original entry on oeis.org

643905, 680061, 720558, 775113, 840501, 878613, 984927
Offset: 1

Views

Author

Zhining Yang, Jan 16 2009

Keywords

Comments

a(5) is also the number of A074205

Examples

			840501^5=419460598737334268928156702501, which contains exactly 3 times of each digit 0-9. Total 7 terms

Crossrefs

A054038 A074205 A154532 A154566 A154818

Programs

  • Mathematica
    Select[Range[630972,999978],Union[DigitCount[#^5]]=={3}&] (* Harvey P. Dale, May 01 2021 *)

A154874 Numbers k such that k^3 contains every digit exactly twice.

Original entry on oeis.org

2158479, 2190762, 2205528, 2219322, 2301615, 2330397, 2336268, 2345811, 2358828, 2359026, 2367609, 2388534, 2389119, 2389638, 2397132, 2428986, 2504736, 2524974, 2536152, 2583258, 2590125, 2607222, 2620827, 2622012, 2647866, 2649369, 2658636, 2671593
Offset: 1

Views

Author

Zhining Yang, Jan 16 2009

Keywords

Comments

This sequence has 138 terms.

Examples

			2358828^3 = 13124683009764879552, which contains each digit 0..9 exactly twice.

Links

Crossrefs

Cf. A054038, A074205, A154532, A154566, A154871, A154873.

Programs

  • Maple
    lim:=floor((10^20)^(1/3)): for j from ceil((10^19)^(1/3)) to lim do d:=convert(j^3,base,10): doubdig:=true: for k from 0 to 9 do if(numboccur(d,k)<>2)then doubdig:=false:break: fi: od: if(doubdig)then print(j); fi: od: # Nathaniel Johnston, May 28 2011
  • Mathematica
    With[{cmin=Ceiling[Surd[10^19,3]],cmax=Floor[Surd[10^20,3]]},Select[ Range[ cmin, cmax], Union[ DigitCount[#^3]]=={2}&]] (* Harvey P. Dale, Nov 17 2018 *)

A217368 Smallest number having a power that in decimal has exactly n copies of all ten digits.

Original entry on oeis.org

32043, 69636, 643905, 421359, 320127, 3976581, 47745831, 15763347, 31064268, 44626422, 248967789, 85810806, 458764971, 500282265, 2068553967, 711974055, 2652652791, 901992825, 175536645, 3048377607, 3322858521, 1427472867, 3730866429, 9793730157
Offset: 1

Views

Author

James G. Merickel, Oct 01 2012

Keywords

Comments

The exponents that produce the number with a fixed number of copies of each digit are listed in sequence A217378. See there for further comments.
Since we allow A217378(n)=1, the sequence is well defined, with the upper bound a(n) <= 100...99 ~ 10^(10n-1) (n copies of each digit, sorted in increasing order, except for one "1" permuted to the first position). - M. F. Hasler, Oct 05 2012
What is the minimum value of a(n)? Can it be proved that a(n) > 2 for all n? - Charles R Greathouse IV, Oct 16 2012

Examples

			The third term raised to the fifth power (A217378(3)=5), 643905^5 = 110690152879433875483274690625, has three copies of each digit (in its decimal representation), and no number smaller than 643905 has a power with this feature.

Crossrefs

Cf. A020666, A054038, A054039, A066825, A067635, A074205, A156977, A217378.

Programs

  • Mathematica
    f[n_] := Block[{k = 2, t = Table[n, {10}], r = Range[0, 9]}, While[c = Count[ IntegerDigits[k^Floor[ Log[k, 10^(10 n)]]], #] & /@ r; c != t, k++]; k] (* Robert G. Wilson v, Nov 28 2012 *)
  • PARI
    is(n,k)=my(v);for(e=ceil((10*n-1)*log(10)/log(k)), 10*n*log(10)/log(k), v=vecsort(digits(k^e)); for(i=1,9,if(v[i*n]!=i-1 || v[i*n+1]!=i, return(0))); return(1)); 0
a(n)=my(k=2); while(!is(n,k),k++); k \\ Charles R Greathouse IV, Oct 16 2012

Extensions

a(13)-a(14) from James G. Merickel, Oct 06 2012 and Oct 08 2012
a(15)-a(16) from Charles R Greathouse IV, Oct 17 2012
a(17)-a(19) from Charles R Greathouse IV, Oct 18 2012
a(20) from Charles R Greathouse IV, Oct 22 2012
a(21)-a(24) from Giovanni Resta, May 05 2017

A154818 Numbers k such that k^4 contains every digit exactly twice.

Original entry on oeis.org

69636, 70215, 77058, 80892
Offset: 1

Views

Author

Zhining Yang, Jan 15 2009

Keywords

Comments

77058^4 = 35259076387041812496, which contains 2 of each digit 0-9. There are just 4 terms.

Crossrefs

Cf. A054038, A074205, A154532, A154566.

Extensions

Keywords fini and full added. - R. J. Mathar, Jan 17 2009

A154875 Numbers k such that k^4 contains every digit exactly 3 times.

Original entry on oeis.org

17824719, 17940018, 18027474, 18197931, 18326025, 18798396, 18915888, 18929424, 19027455, 19149462, 19180275, 19196064, 19235673, 19311297, 19322913, 19324275, 19328322, 19455918, 19522575, 19757886, 19793664
Offset: 1

Views

Author

Zhining Yang, Jan 16 2009

Keywords

Examples

			22807116 ^ 4 = 270571148920443982076865351936, which contains exactly 3 times of each digit 0-9.

Links

Crossrefs

Cf. A054038, A074205, A154532, A154566, A154871, A154873, A154874.

Programs

  • Mathematica
    Select[Range[17824000,31608000],Union[Tally[IntegerDigits[#^4]][[All,2]]]=={3}&] (* Harvey P. Dale, Dec 24 2016 *)
  • PARI
    is(n) = my(v=vector(10), d=digits(n^4)); if(#d!=30,return(0)); for(i=1, #d, v[d[i]+1]++; if(v[d[i]+1] > 3, return(0))); 1 \\ David A. Corneth, Aug 19 2025

A178960 Numbers n such that n! contains every digit at least once.

Original entry on oeis.org

23, 27, 31, 33, 34, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101
Offset: 1

Views

Author

Michel Lagneau, Dec 31 2010

Keywords

Examples

			23 is in the sequence because 23! = 25852016738884976640000 contains every
  digit at least once.

Crossrefs

Cf. A178929, A054038, A156977, A054038, A074205, A020666.

Programs

  • Magma
    [n: n in [0..101] | Seqset(Intseq(Factorial(n))) eq {0..9}]; // Bruno Berselli, May 17 2011
  • Maple
    with(numtheory):Digits:=200:B:={0,1,2,3,4,5,6,7,8,9}: T:=array(1..250) : for
  p from 1 to 200 do:ind:=0:n:=p!:l:=length(n):n0:=n:s:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v : T[m]:=u:od: A:=convert(T,set):z:=nops(A):if A intersect B = B and ind=0 then ind:=1: printf(`%d, `,p):else fi:od:
  • Mathematica
    Select[Range[101], Length[Union[IntegerDigits[#!]]] == 10 &]

A217535 Least number having in its decimal representation each digit n times.

Original entry on oeis.org

1023456789, 10012233445566778899, 100011222333444555666777888999, 1000011122223333444455556666777788889999, 10000011112222233333444445555566666777778888899999, 100000011111222222333333444444555555666666777777888888999999
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2012

Keywords

Links

Crossrefs

Cf. A050278, A051018, A049363, A074205, A154566, A204047, A020666, A020667, A061604, A180489.
A subsequence of A171102.

Programs

  • Maple
    a:= n-> parse(cat(1,0$n,1$(n-1),seq(i$n, i=2..9))):
seq(a(n), n=1..10);  # Alois P. Heinz, Jun 25 2017
  • PARI
    A217535(n)=sum(d=1,9,10^(n-(d==1))\9*d*10^(n*(9-d)))+10^(10*n-1)

Formula

a(n) ~ 10^(10n-1). See PARI code for an exact formula.

A154876 10-digit numbers n such that n^16 contains every digit exactly 16 times.

Original entry on oeis.org

8691229761, 8776040742, 8800099059, 8812428855, 8813522223, 8815323864, 8823675177, 8886940968, 9239038038, 9324907263, 9480130515, 9500938647, 9643844169, 9801034758, 9857840688, 9872688021, 9962545842, 9970902252
Offset: 1

Views

Author

Zhining Yang, Jan 16 2009

Keywords

Comments

The search program was provided by wuxinren(http://bbs.emath.ac.cn/space-uid-80.html): http://bbs.emath.ac.cn/attachment.php?aid=697&k=37ef434325a887e1a6f268d69d06192a&t=1232126232

Examples

			8691229761^16=1059984945135973085116625441940958734567890938937942910046410302827750560860737374626331724228885721853160790705924439371252226476405367618058329962361885148161 means that 16th power of 8691229761 has all digit(0-9) each for 16 times exactly

Links

Crossrefs

Cf. A154874 A054038 A074205 A154532 A154566 A154871 A154873
Showing 1-9 of 9 results.

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

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