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.

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A030706 Decimal expansion of 11^n contains no zeros (probably finite).

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 41
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

See A195946 for the actual powers 11^n. - M. F. Hasler, Dec 17 2014
It appears that 41 is also the largest integer n such that 11^n is not pandigital, cf. A272269. - M. F. Hasler, May 18 2017

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, Mar 07 2014
  • Eric Weisstein's World of Mathematics, Zero

Crossrefs

For other zeroless powers x^n, see A238938, A238939, A238940, A195948, A238936, A195908 (x=7), A245852, A240945 (k=9), A195946 (x=11), A245853 (x=12), A195945 (x=13); A195942, A195943, A103662.
For the corresponding exponents, see A007377, A030700, A030701, A008839, A030702, A030703, A030704, A030705, A030706 (this), A195944.
For other related sequences, see A052382, A027870, A102483, A103663.

Programs

  • Mathematica
    Select[Range[0,41],DigitCount[11^#,10,0]==0&] (* Harvey P. Dale, Dec 31 2020 *)
  • PARI
    for(n=0,99,vecmin(digits(11^n))&&print1(n",")) \\ M. F. Hasler, Mar 08 2014

Extensions

Offset corrected and initial term 0 added by M. F. Hasler, Sep 25 2011
Further edits by M. F. Hasler, Dec 17 2014

A272322 Numbers n such that n^n does not contain all ten decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 27, 28, 30, 34, 40, 100, 1000, 10000, 100000, 1000000
Offset: 1

Views

Author

Altug Alkan, Apr 25 2016

Keywords

Comments

A240963 is a subsequence.
A011557 is a subsequence. So this sequence is obviously infinite.
Conjecture: the only values > 40 are the powers of 10. - Franklin T. Adams-Watters, Apr 29 2016

Examples

			27 is a term because 27^27 = 443426488243037769948249630619149892803 does not contain digit 5.
28 is a term because 28^28 = 33145523113253374862572728253364605812736 does not contain digit 9.

Crossrefs

Cf. A000312, A011557, A130696, A171102, A240963, A272269.

Programs

  • Mathematica
    {0}~Join~Select[Range[10^4], Times @@ DigitCount[#^#] == 0 &] (* Michael De Vlieger, Apr 25 2016 *)
  • PARI
    isA171102(n) = 9<#vecsort(Vecsmall(Str(n)), , 8);
lista(nn) = for(n=0, nn, if(!isA171102(n^n), print1(n, ", ")));
  • PARI
    is(n)=#Set(digits(n^n))<=9 \\ Charles R Greathouse IV, Apr 29 2016

Extensions

a(31) from Charles R Greathouse IV, Apr 29 2016
a(32) from Charles R Greathouse IV, May 03 2016
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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