A385937 a(n) is the starting position of the second occurrence of a string of the initial n binary digits of Pi in the binary expansion of Pi.

1, 12, 16, 48, 77, 246, 246, 418, 418, 513, 513, 513, 513, 44458, 109628, 201504, 201504, 260229, 260229, 260229, 260229, 5195536, 5195536, 5195536, 16400799, 71861116, 71861116, 71861116, 88885576, 88885576, 465466168, 465466168, 2612839361, 2612839361, 5728737753, 5728737753, 141859217232

Offset: 1

Author

Jason A. Doucette, Jul 12 2025

Keywords

• nonn
• base

Comments

Digit positions are numbered starting at 0 for the first 1 of binary Pi = 11.001..., then position 1 for integer bit, and so on.

Terms a(1)..a(37) found in first 166096404750 binary digits.

a(38) > 1.66*10^11.

Links

• Jason Doucette, Pi Inside Pi, July 12, 2025.

Crossrefs

Cf. A004601 (Pi in binary), A081876 (decimal Pi-inside-Pi), A385936 (hexadecimal Pi-inside-Pi).