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 1-2 of 2 results.

A240962 Number of zeros in the decimal expansion of n^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 1, 2, 2, 3, 2, 2, 1, 2, 1, 21, 1, 0, 5, 2, 3, 6, 3, 1, 1, 32, 6, 5, 7, 7, 3, 3, 6, 8, 6, 42, 5, 6, 10, 10, 5, 11, 4, 12, 11, 53, 5, 6, 12, 10, 8, 11, 15, 9, 5, 64, 12, 15, 14, 16, 13, 12, 13, 9, 16, 79, 12, 16, 15, 12, 14, 15
Offset: 1

Views

Author

Anthony Sand, Aug 05 2014

Keywords

Examples

			a(1) = zerocount(1^1) = zerocount(1) = 0.
a(8) = zerocount(8^8) = zerocount(16777216) = 0.
a(9) = zerocount(9^9) = zerocount(387420489) = 1.
a(10) = zerocount(10^10) = zerocount(10000000000) = 10.
		

Crossrefs

Programs

  • Maple
    seq(numboccur(0,convert(n^n,base,10)), n=1 .. 100); # Robert Israel, Aug 05 2014
  • Mathematica
    Map[Count[IntegerDigits[#^#], 0] &, Range[2, 100]] (* Michael De Vlieger, Aug 06 2014 *)
  • PARI
    a(n) = my(d = digits(n^n)); sum(i=1, #d, ! d[i]); \\ Michel Marcus, Aug 10 2014
  • Python
    for n in range(1,10**3):
      print(str(n**n).count('0'),end=', ') # Derek Orr, Aug 05 2014
    

Formula

a(n) = A055641(A000312(n)). - Michel Marcus, Aug 07 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

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
Showing 1-2 of 2 results.