A385994 Lexicographically greatest increasing expansion Pi = Sum_{n>=0} a(n)/10^n, where a(n+1) >= a(n).

2, 10, 12, 19, 23, 26, 29, 32, 40, 48, 50, 53, 53, 61, 62, 65, 74, 75, 79, 85, 86, 92, 95, 102, 111, 111, 115, 119, 128, 133, 134, 139, 144, 146, 151, 160, 165, 172, 179, 186, 190, 195, 197, 201, 206, 215, 219, 222, 229, 234, 243, 248, 250, 253, 261, 269, 276, 283, 287

Offset: 0

Author

Pierre-Alain Sallard, Jul 14 2025

Keywords

• nonn
• base
• easy

Comments

Each successive term is maximal consistent with the sum approaching Pi from below.

Each difference d = a(n) - a(n-1) (and reckoning an a(-1)=0) effectively repeats in all subsequent terms and so contributes (10/9)*d/10^n into the sum, and for that reason those differences are the decimal digits of (9/10)*Pi and the terms are partial sums of those digits.

Links

• Pierre-Alain Sallard, Proof

Crossrefs

Cf. A000796.

Partial sums of A229939.

Programs

Mathematica

a[n_]:=Sum[Part[RealDigits[9*Pi, n+1][[1]],i],{i,1,n+1}]; Array[a,59,0] (* Stefano Spezia, Jul 14 2025 *)

Formula

a(n) = Sum_{i=0..n} A229939(i+1).