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 1-3 of 3 results.

A046412 Lengths of nonsquarefree repunits.

Original entry on oeis.org

9, 18, 22, 27, 36, 42, 44, 45, 54, 63, 66, 72, 78, 81, 84, 88, 90, 99, 108, 110, 111, 117, 126, 132, 135, 144, 153, 154, 156, 162, 168, 171, 176, 180, 189, 198, 205, 207, 210, 216, 220, 222, 225, 234, 242, 243, 252, 261, 264, 270, 272, 279, 286, 288, 294, 297, 306, 308, 312, 315, 324, 330, 333, 336, 342, 351, 352
Offset: 1

Views

Author

Patrick De Geest, Jul 15 1998

Keywords

Comments

This is the set of all positive multiples of all positive members of A087094. What is the asymptotic density of this set? - Jeppe Stig Nielsen, Dec 28 2015

Links

Crossrefs

Cf. A000042, A004022, A046053, A084006, A087094.

Programs

  • Maple
    remove(t -> numtheory:-issqrfree((10^t-1)/9), [$1..90]); # Robert Israel, Dec 30 2015
  • Mathematica
    Select[Range[300],!SquareFreeQ[(10^#-1)/9]&] (* Harvey P. Dale, Jun 26 2013 *)
  • PARI
    isok(n) = ! issquarefree((10^n-1)/9); \\ Michel Marcus, Dec 31 2015

Formula

a(n)=k where (10^k-1)/9 is not squarefree. - Ray Chandler, Aug 10 2003

Extensions

Terms to a(60) from Ray Chandler, Aug 10 2003
a(61)-a(67) from Max Alekseyev, Apr 29 2022

A077571 Squarefree numbers obtained by repeating a single digit.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 11, 22, 33, 55, 66, 77, 111, 222, 555, 777, 1111, 2222, 3333, 5555, 6666, 7777, 11111, 22222, 33333, 55555, 66666, 77777, 111111, 222222, 555555, 1111111, 2222222, 3333333, 5555555, 6666666, 7777777, 11111111, 22222222, 33333333
Offset: 1

Views

Author

Amarnath Murthy, Nov 11 2002

Keywords

Comments

From Robert Israel, Feb 26 2019: (Start)
If A002275(n) is not in the sequence, then there are no terms of length n.
2*A002275(n) and 5*A002275(n) are in the sequence if and only if A002275(n) is in the sequence.
3*A002275(n) and 6*A002275(n) are in the sequence if and only if A002275(n) is in the sequence and n is not divisible by 3.
7*A002275(n) is in the sequence if and only if A002275(n) is in the sequence and n is not divisible by 6. (End)
Intersection of A005117 and A010785. - Felix Fröhlich, Feb 26 2019

Examples

			66 and 6666 are members but 666 is not.

Links

Crossrefs

Cf. A002275, A005117, A010785, A087094.

Programs

  • Maple
    g:= proc(n) local r;
  r:= (10^n-1)/9;
  if not numtheory:-issqrfree(r) then NULL
  elif n mod 6 = 0 then r, 2*r, 5*r
  elif n mod 3 = 0 then r, 2*r, 5*r, 7*r
  else r, 2*r, 3*r,5*r, 6*r, 7*r
  fi
end proc:
seq(g(n),n=1..10); # Robert Israel, Feb 26 2019
  • PARI
    is(n) = n>0 && vecmin(digits(n))==vecmax(digits(n)) && issquarefree(n) \\ Felix Fröhlich, Feb 26 2019

Extensions

Corrected and extended by Ray Chandler, Aug 12 2003
Offset changed by Robert Israel, Feb 26 2019

A077572 Nonsquarefree numbers obtained by repeating a single digit.

Original entry on oeis.org

4, 8, 9, 44, 88, 99, 333, 444, 666, 888, 999, 4444, 8888, 9999, 44444, 88888, 99999, 333333, 444444, 666666, 777777, 888888, 999999, 4444444, 8888888, 9999999, 44444444, 88888888, 99999999, 111111111, 222222222, 333333333, 444444444
Offset: 1

Views

Author

Amarnath Murthy, Nov 11 2002

Keywords

Examples

			666 and 111111111 are members but 66, 1111 etc. are not.

Crossrefs

Cf. A077571, A087094.
Subsequence of A013929 and A035132.

Programs

  • Mathematica
    Select[Flatten[Table[FromDigits[PadRight[{},i,n]],{i,9},{n,9}]],!SquareFreeQ[#]&] (* Harvey P. Dale, Jan 22 2013 *)
  • Python
    from sympy.ntheory.factor_ import core
def repsthru(maxd):
  yield from (int(di*d) for d in range(1, maxd+1) for di in "123456789")
def okrep(r): return r > 3 and core(r, 2) != r
print(list(filter(okrep, repsthru(9)))) # Michael S. Branicky, Apr 08 2021

Extensions

Corrected and extended by Ray Chandler, Aug 12 2003
Offset changed by Andrew Howroyd, Sep 29 2024
Showing 1-3 of 3 results.

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

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