A247345 a(1) = 16. For n > 1, a(n) is the position of the first occurrence of a(n-1) after the decimal point in the decimal expansion of Pi.

16, 40, 70, 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, 40, 70, 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, 40, 70, 96

Offset: 1

Author

Felix Fröhlich, Jul 26 2015

Keywords

• nonn
• base

Comments

After the first term, the sequence enters a repeating cycle of length 20.

According to the information on the website of Anderson, this sequence was discovered earlier by Dan Sikorsky.

First element a(1) = 61 leads after seven steps 61, 219, 716, 39, 43, 23, 16, ... into the same repeating cycle, same with a(1) = 71 after five steps 71, 39, 43, 23, 16, ... - Martin Renner, Feb 22 2020

Links

• D. Andersen, Loop Sequences within Pi, The Pi-Search Page.

Crossrefs

Cf. A000796, A097614.

Programs

Mathematica

L={16}; pi=ToString[ FromDigits@ RealDigits[Pi-3, 10, 10^5 ][[1]]]; Do[
AppendTo[L, StringPosition[ pi, ToString@ Last@ L, 1][[1, 1]]], {23}]; L (* Giovanni Resta, Jul 26 2015 *)