A332756 A loop sequence within Pi. Let a(1) = 19. For n > 1, a(n+1) is the position of the first occurrence of a(n) after the decimal point in the decimal expansion of Pi.

19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37, 46, 19, 37

Offset: 1

Author

Martin Renner, Feb 22 2020

Keywords

• easy
• nonn
• base

Comments

The sequence has a repeating cycle of length 3.

Links

• David G. Andersen, The Pi-Search Page.
• Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020).
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A000796, A057680, A097614, A247345.

Programs

Mathematica

PadRight[{}, 100, {19, 37, 46}] (* Paolo Xausa, Apr 27 2024 *)

Formula

From Stefano Spezia, Feb 22 2020: (Start)

O.g.f.: x*(19 + 37*x + 46*x^2)/(1 - x^3).

E.g.f.: 34*(cosh(x) + sinh(x)) - 46 - 6*exp(-x/2)*(sqrt(3)*sin(sqrt(3)*x/2) - 2*cos(sqrt(3)*x/2)).

a(n) = a(n-3) for n > 3. (End)