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

0,3

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

Formula

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

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 *)

Prog

(Scheme, two versions)
;; Implemented with a loop:
(define (A276336 n) (let loop ((n n) (m 0)) (if (zero? n) m (loop (A276335 n) (max m (A276333 n))))))
;; As a recurrence:
(definec (A276336 n) (if (zero? n) n (max (A276333 n) (A276336 (A276335 n)))))

Crossrefs

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

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

Sequence in context: A276327 A007884 A190593 * A212811 A338854 A330957

Adjacent sequences: A276333 A276334 A276335 * A276337 A276338 A276339

Keyword

nonn,base

Author

Antti Karttunen, Aug 30 2016

Status

approved