A344887 - OEIS

%I #13 Jun 02 2021 22:14:07

%S 2,2,2,2,2,4,2,2,2,3,4,5,2,3,2,2,2,5,3,6,4,3,3,5,2,3,3,3,2,7,2,2,2,6,

%T 6,6,3,4,7,3,3,4,4,6,7,7,7,7,2,7,5,8,4,4,3,5,2,4,4,8,2,4,2,2,2,9,3,3,

%U 9,9,9,10,3,8,9,3,3,9,3,3,3,3,10,10,4,4

%N a(n) is the least base k >= 2 that the base-k digits of n are nonincreasing.

%H Rémy Sigrist, <a href="/A344887/b344887.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) <= A000196(n) + 2.

%F a(n) <= 10 for any n in A009996.

%F a(n) = 2 iff n belongs to A023758.

%e For n = 258:

%e - we have:

%e      b  258 in base b  Nonincreasing?

%e      -  -------------  --------------

%e      2      100000010  No

%e      3         100120  No

%e      4          10002  No

%e      5           2013  No

%e      6           1110  Yes

%e - so a(258) = 6.

%t Table[k=1;While[AnyTrue[Differences@IntegerDigits[n,++k],#>0&]];k,{n,0,100}] (* _Giorgos Kalogeropoulos_, Jun 02 2021 *)

%o (PARI) a(n) = { for (b=2, oo, my (d=digits(n, b)); if (d==vecsort(d,,4), return (b))) }

%o (Python) # with library / without (faster for large n)

%o from sympy.ntheory import digits

%o def is_nondec(n, b): d = digits(n, b)[1:]; return d == sorted(d)[::-1]

%o def is_nondec(n, b):

%o   if n < b: return True

%o   n, r = divmod(n, b)

%o   while n >= b:

%o     (n, r), lastd = divmod(n, b), r

%o     if r < lastd: return False

%o   return n >= r

%o def a(n):

%o   for b in range(2, n+3):

%o     if is_nondec(n, b): return b

%o print([a(n) for n in range(86)]) # _Michael S. Branicky_, Jun 01 2021

%Y Cf. A000196, A009996, A023758, A273040.

%K nonn,base

%O 0,1

%A _Rémy Sigrist_, Jun 01 2021