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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 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

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)