cp's OEIS Frontend

A356384 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) = x_n(b-1) minus the sum of digits of x_n(b-1) in base b; a(n) is the least b such that x_n(b) = 0.

%I A356384 #13 Aug 07 2022 15:36:45
%S A356384 1,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%T A356384 8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,11,11,11,
%U A356384 11,11,11,12,12,12,12,12,12,12,12,13,13,13,13,13
%N A356384 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) = x_n(b-1) minus the sum of digits of x_n(b-1) in base b; a(n) is the least b such that x_n(b) = 0.
%C A356384 This sequence is well defined: for any n >= 0: if x_n(b) > 0, then x_n(b+1) < x_n(b), and we must eventually reach 0.
%C A356384 This sequence is weakly increasing; this is related to the fact that for any base b > 1, k -> (k minus the sum of digits of k in base b) is weakly increasing.
%C A356384 Note that some values (like 7) do not appear in this sequence (see also A356386).
%H A356384 Rémy Sigrist, <a href="/A356384/b356384.txt">Table of n, a(n) for n = 0..10000</a>
%H A356384 Rémy Sigrist, <a href="/A356384/a356384.png">Colored scatterplot of (n, x_n(b)) for n <= 1000 and b = 1..a(n)</a> (the color is function of b)
%H A356384 Rémy Sigrist, <a href="/A356384/a356384.gp.txt">PARI program</a>
%e A356384 For n = 42:
%e A356384 - we have:
%e A356384       b  x(b)
%e A356384       -  ----
%e A356384       1    42
%e A356384       2    39
%e A356384       3    36
%e A356384       4    33
%e A356384       5    28
%e A356384       6    20
%e A356384       7    12
%e A356384       8     7
%e A356384       9     0
%e A356384 - so a(42) = 9.
%o A356384 (PARI) See Links section.
%Y A356384 Cf. A011371, A066568, A071542, A261231, A344853, A356386.
%K A356384 nonn,base
%O A356384 0,2
%A A356384 _Rémy Sigrist_, Aug 05 2022