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A109381 Maximum digit of n^2 written in factorial base. 2
0, 1, 2, 1, 2, 1, 2, 2, 2, 3, 4, 1, 1, 2, 3, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 1, 2, 1, 2, 2, 2, 3, 3, 4, 4, 5, 2, 3, 2, 2, 3, 3, 4, 4, 5, 3, 3, 3, 4, 3, 4, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 1, 1, 2, 3, 4, 2, 2, 3, 4, 5, 3, 2, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 2, 3, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: lim_{n->infinity} a(n) = infinity. If true, convergence is very slow, since a(1183893) = 1. Sequence is certainly unbounded, since for n >= 4, there is always a square between n*n! and (n+1)!.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20954

EXAMPLE

4^2 = 16 = 2*6+2*2 = 220(factorial base), so a(4) = max(2,2,0) = 2.

MAPLE

b:= proc(n, i) local r; `if`(n<i, n,

      max(b(iquo(n, i, 'r'), i+1), r))

    end:

a:= n-> b(n^2, 2):

seq(a(n), n=0..188);  # Alois P. Heinz, Mar 28 2018

MATHEMATICA

Block[{nn = 105^2, r}, r = Reverse@ Most@ NestWhileList[# + 1 &, 2, #! < nn &]; Array[Max@ IntegerDigits[#^2, MixedRadix@ r] &, Sqrt@ nn, 0]] (* Michael De Vlieger, Jan 01 2019 *)

PROG

(PARI) f(n, p=2) = if( n<p, n, f( n\p, p+1 )*10 + n%p ); \\ A007623

a(n) = my(dfb=digits(f(n^2))); if (#dfb, vecmax(dfb), 0); \\ Michel Marcus, Mar 28 2018

CROSSREFS

Cf. A007623, A108731, A301872.

Indices of 1's in this sequence are A014597.

Sequence in context: A133989 A029398 A025817 * A058506 A325509 A324117

Adjacent sequences:  A109378 A109379 A109380 * A109382 A109383 A109384

KEYWORD

easy,nonn,base

AUTHOR

Franklin T. Adams-Watters, Aug 25 2005

STATUS

approved

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Last modified October 16 16:06 EDT 2019. Contains 328101 sequences. (Running on oeis4.)