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 1-8 of 8 results.

A177195 Fibonacci numbers whose decimal expansion does not contain the digit 1.

Original entry on oeis.org

0, 2, 3, 5, 8, 34, 55, 89, 233, 377, 987, 2584, 6765, 28657, 46368, 75025, 832040, 3524578, 5702887, 9227465, 63245986, 433494437, 4807526976, 7778742049, 27777890035288, 5527939700884757, 2427893228399975082453, 22698374052006863956975682
Offset: 1

Views

Author

Carmine Suriano, May 04 2010

Keywords

Comments

The probability that Fibonacci(n) contains no digit 1 decreases to 0 as n goes to infinity. Seems that its maximum value is Fibonacci(211) having 44 digits, none of them is 1.

Examples

			34 is a term since 34 is a Fibonacci number having no 1's. [corrected by _D. S. McNeil_, Nov 12 2010]

Crossrefs

Cf. A000045, A177194, A176253.

Programs

  • Magma
    [Fibonacci(n): n in [0..150] |  not 1 in Intseq(Fibonacci(n))]; // Vincenzo Librandi, May 09 2019
  • Mathematica
    Select[Fibonacci[Range[0, 150]], DigitCount[#, 10, 1]==0&] (* Harvey P. Dale, Apr 18 2019 *)

Extensions

a(1)=0 added by Alois P. Heinz, May 04 2019

A177231 Fibonacci numbers whose decimal expansion does not contain any digit "2".

Original entry on oeis.org

0, 1, 3, 5, 8, 13, 34, 55, 89, 144, 377, 610, 987, 1597, 4181, 6765, 10946, 17711, 46368, 196418, 317811, 39088169, 165580141, 433494437, 701408733, 1134903170, 1836311903, 17167680177565, 117669030460994, 806515533049393, 99194853094755497, 160500643816367088
Offset: 1

Views

Author

Carmine Suriano, May 05 2010

Keywords

Comments

The probability that Fibonacci(n) contains no 2's goes to zero as n grows to infinity. The maximum term is possibly Fibonacci(101) having 21 digits, none of them being "2".

Examples

			a(5) = 8 is the 5th Fibonacci number having no digit 2's.

Crossrefs

Cf. A000045, A177194, A177195, A176253.

Programs

  • Magma
    [0] cat [Fibonacci(n): n in [2..150] | not 2 in Intseq(Fibonacci(n))]; // Vincenzo Librandi, May 09 2019
  • Maple
    F:= combinat[fibonacci]:
q:= n-> not(2 in convert(n, base, 10)):
select(q, {F(n)$n=0..101})[];  # Alois P. Heinz, May 06 2019
  • Mathematica
    Join[{0}, Select[Fibonacci[Range[2, 50]], DigitCount[#, 10, 2]==0&]] (* Harvey P. Dale, Oct 01 2017 *)

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010
a(1) changed from 1 to 0 by Alois P. Heinz, May 06 2019

A177245 Fibonacci numbers whose decimal expansion does not contain any digit 3.

Original entry on oeis.org

0, 1, 2, 5, 8, 21, 55, 89, 144, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 75025, 196418, 514229, 5702887, 9227465, 24157817, 165580141, 267914296, 4807526976, 7778742049, 12586269025, 86267571272, 591286729879, 956722026041, 1548008755920
Offset: 1

Views

Author

Carmine Suriano, May 06 2010

Keywords

Comments

Probability that Fib(n) contains no 3's decreases to zero as n goes to infinity. I suppose that the maximum number is Fib(223) having 47 digits, none of them being a "3".

Examples

			a(6)=21 since 21 is the 6th Fibonacci having no 3's.

Crossrefs

Cf. A000045, A177194, A177195, A177231, A176253

Programs

  • Magma
    [0] cat [Fibonacci(n): n in [2..150] | not 3 in Intseq(Fibonacci(n))]; // Vincenzo Librandi, May 09 2019
  • Mathematica
    Join[{0}, Select[Fibonacci[Range[2, 60]], DigitCount[#, 10, 3]==0&]] (* Vincenzo Librandi, May 09 2019 *)

Extensions

a(1) changed from 1 to 0 by Vincenzo Librandi, May 09 2019

A177246 Fibonacci numbers whose decimal expansion does not contain any digit 4.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 55, 89, 233, 377, 610, 987, 1597, 6765, 17711, 28657, 75025, 121393, 317811, 2178309, 5702887, 39088169, 1836311903, 2971215073, 12586269025, 32951280099, 53316291173, 86267571272, 591286729879
Offset: 1

Views

Author

Carmine Suriano, May 06 2010

Keywords

Comments

Probability that Fib(n) contains no 4's goes to zero as n grows to infinity. I suppose that the maximum number is Fib(114) having 24 digits, none of them being a "4".

Examples

			a(9)=55 is the 9th Fibonacci having no digit 4's.

Links

Crossrefs

Cf. A000045, A177194, A177195, A177231, A177245, A176253.

Programs

  • Maple
    remove(t -> has(convert(t,base,10),4), map(combinat:-fibonacci, [$1..1000])); # Robert Israel, Dec 13 2018
  • Mathematica
    Select[Fibonacci@Range@114, !MemberQ[IntegerDigits[#], 4] &] (* Amiram Eldar, Dec 13 2018 *)

A177247 Fibonacci numbers Fib(n) whose decimal expansion does not contain any digit 6.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 987, 1597, 2584, 4181, 17711, 75025, 121393, 317811, 514229, 832040, 2178309, 3524578, 5702887, 14930352, 24157817, 102334155, 433494437, 701408733, 1134903170, 2971215073, 7778742049
Offset: 1

Views

Author

Carmine Suriano, May 06 2010

Keywords

Comments

Probability that Fib(n) contains no 6's goes to zero as n grows to infinity. I suppose the maximum number is F(258) having 54 digits with no 6's.

Examples

			a(7)=13 since it is the 7th Fibonacci having no 6's

Crossrefs

Cf. A000045, A177194, A177195, A177231, A177245, A177246, A176253

Programs

  • Mathematica
    Select[Fibonacci[Range[100]],DigitCount[#,10,6]==0&] (* Harvey P. Dale, Aug 26 2023 *)

A177372 Fibonacci numbers whose decimal expansion does not contain any digit 7.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 610, 2584, 4181, 10946, 46368, 121393, 196418, 514229, 832040, 1346269, 14930352, 39088169, 63245986, 102334155, 165580141, 1836311903, 12586269025, 32951280099, 139583862445, 365435296162
Offset: 1

Views

Author

Carmine Suriano, May 07 2010

Keywords

Comments

Probability that Fib(n) contains no digit 7 goes to zero as n grows to infinity. I suppose that the maximum number is Fib(224) having 47 digits.

Examples

			a(14)=610 since it is the 14th Fibonacci containing no 7's.

Crossrefs

Cf. A000045, A177194, A177195, A177231, A177245, A177246, A176253, A177247

Programs

  • Mathematica
    Select[Fibonacci[Range[100]],DigitCount[#,10,7]==0&] (* Harvey P. Dale, Dec 13 2014 *)

A177374 Fibonacci numbers whose decimal expansion does not contain any digit 8.

Original entry on oeis.org

1, 1, 2, 3, 5, 13, 21, 34, 55, 144, 233, 377, 610, 1597, 6765, 10946, 17711, 75025, 121393, 514229, 1346269, 9227465, 14930352, 102334155, 267914296, 433494437, 1134903170, 2971215073, 20365011074, 53316291173, 365435296162
Offset: 1

Views

Author

Carmine Suriano, May 07 2010

Keywords

Comments

Probability that Fib(n) contains no 8's goes to zero as n grows to infinity. I suppose that the maximum number is Fib(142) having 30 digits.
The above conjecture is true up through Fib(100,000) which has 20,800 digits. - Harvey P. Dale, Dec 31 2013

Examples

			a(8)=34 since it is the 8th Fibonacci having no 8's

Crossrefs

Cf. A000045, A177194, A177195, A177231, A177245, A177246, A176253, A177247, A177372

Programs

  • Mathematica
    Select[Fibonacci[Range[100]],DigitCount[#,10,8]==0&] (* Harvey P. Dale, Dec 31 2013 *)

A177376 Fibonacci numbers whose decimal expansion does not contain any digit 9.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, 233, 377, 610, 2584, 4181, 6765, 17711, 28657, 46368, 75025, 317811, 832040, 3524578, 5702887, 24157817, 102334155, 165580141, 701408733, 20365011074, 86267571272, 225851433717, 17167680177565
Offset: 1

Views

Author

Carmine Suriano, May 07 2010

Keywords

Comments

The probability that Fib(n) contains no 9's goes to zero as n grows to infinity. It appears that the largest term is F(188). [Corrected by Jon E. Schoenfield, May 08 2010]

Examples

			a(11)=144 since it is the 11th Fibonacci containing no 9's

Crossrefs

Cf. A000045, A177194, A177195, A177231, A177245, A177246, A176253, A177247, A177272, A177372, A177374

Programs

  • Mathematica
    Select[Fibonacci[Range[100]],DigitCount[#,10,9]==0&] (* Harvey P. Dale, Jan 22 2014 *)
Showing 1-8 of 8 results.

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