A216638 First appearance of the Fibonacci numbers in the decimals of Pi.

1, 1, 6, 9, 4, 11, 110, 93, 86, 130, 11, 1638, 229, 3056, 268, 1510, 10118, 11477, 727, 17711, 83295, 59861, 22334, 19659, 301848, 977089, 59943, 414086, 536681, 649382, 2729036, 68232754, 17793212, 33986473, 695781, 135830965, 117951651, 36978613, 170243036, 366567058

Offset

1,3

Links

Table of n, a(n) for n=1..40.

Peter Trüb, 22.4 trillion digits of pi.

Formula

a(n) = A014777(A000045(n)). - Pontus von Brömssen, Aug 31 2024

Example

Fibonacci(4) is 3, 3 appears for the first time in decimals of Pi in position 9, so a(4) = 9.

Mathematica

(* Determine the decimal digits of Pi following the decimal point. *)
decimalPiDigits[n_] := First@RealDigits[Pi, 10, n, -1];
(* Find the position of first occurrence of 'sublist' in 'list', or Indeterminate if it doesn't occur. *)
firstPosition[sublist_, list_] :=
  With[{p = SequencePosition[list, sublist]},
   If[Length[p] == 0, Indeterminate, First@First@p]];
(* Find the first occurrence of the given digits in the decimal digits of Pi by calculating ever more digits of Pi, as needed. *)
findDigitSequenceInDecimalPiDigits[seq_] :=
  First@NestWhile[
    With[
      {
       numdigits = Max[1, 2*Last[#]] (*
       How many digits will we calculate in this iteration? *)
       },
      {firstPosition[seq, decimalPiDigits[numdigits]], numdigits}
      ] &,
    {Indeterminate, 0},
    Not@*IntegerQ@*First
    ];
(* Find the first 30 entries. *)
Table[findDigitSequenceInDecimalPiDigits[
  IntegerDigits@Fibonacci[n]], {n, 1, 30}]
(* Sidney Cadot, Feb 25 2023 *)

Crossrefs

Cf. A000045, A000796, A014777.

Sequence in context: A273816 A350817 A021063 * A110649 A037024 A309343

Adjacent sequences: A216635 A216636 A216637 * A216639 A216640 A216641

Keyword

nonn,base

Author

Vicente Izquierdo Gomez, Sep 11 2012

Extensions

a(31)-a(40) from Pontus von Brömssen, Aug 31 2024

Status

approved