A276336 The largest digit used when n is written in greedy A001563-base (A276326).

0, 1, 2, 3, 1, 1, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 1, 1, 2, 3, 1, 1, 2

Offset: 0

Author

Antti Karttunen, Aug 30 2016

Keywords

• nonn
• base

Comments

After a(1) = 1 and a(2) = 2, the records occur at positions given by A130744, so that each n >= 3 occurs for the first time at A130744(n-2). This holds because A001563(n) = (n*n!) < A130744(n) = (n+2)*(n*n!) < (n+1)*(n+1)! = A001563(n+1).

First term > 9 occurs thus at A130744(8) = 3225600 with a(3225600)=10.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4320

Crossrefs

Cf. A001563, A130744, A276326, A276333, A276335.

Cf. A276091 (indices of terms <= 1).

Programs

Mathematica

f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; {0}~Join~Table[Max@ f@ n, {n, 120}] (* Michael De Vlieger, Aug 31 2016 *)

Formula

a(0) = 0; for n >= 1, a(n) = max(A276333(n), a(A276335(n))).