cp's OEIS Frontend

A091974 Let R_{k}(n) = the digit reversal of n in base k (R_{k}(n) is written in base 10). a(n) is the number of distinct values of R_{k}(n) arising if k=2,..,n+1.

%I A091974 #13 Jan 29 2020 08:04:58
%S A091974 1,1,2,2,2,3,5,5,5,6,7,9,9,11,11,12,11,14,13,16,16,17,19,21,19,22,22,
%T A091974 21,23,24,27,27,27,29,29,32,29,35,33,36,32,38,37,41,39,41,40,42,41,45,
%U A091974 43,45,46,48,47,49,50,52,52,55,53,57,58,56,57,59,60,61
%N A091974 Let R_{k}(n) = the digit reversal of n in base k (R_{k}(n) is written in base 10). a(n) is the number of distinct values of R_{k}(n) arising if k=2,..,n+1.
%H A091974 Rémy Sigrist, <a href="/A091974/b091974.txt">Table of n, a(n) for n = 0..10000</a>
%H A091974 Rémy Sigrist, <a href="/A091974/a091974.png">Density plot of (n, R_k(n)) for n = 0..1000 and k >= 2</a>
%t A091974 rev[x_, b_]:=FromDigits[Reverse[IntegerDigits[x, b]], b]
%t A091974 Length /@ Union /@ Table[Table[rev[x, b], {b, 2, x + 1}], {x, 1, 200}] (* _Dylan Hamilton_, Oct 16 2010 *)
%o A091974 (PARI) a(n) = #Set(apply(b -> fromdigits(Vecrev(digits(n,b)),b), [2..max(2,n+1)])) \\ _Rémy Sigrist_, Jan 29 2020
%Y A091974 Cf. A004086, A030101-A030108, A056960-A056963, A181385.
%K A091974 nonn,base
%O A091974 0,3
%A A091974 _Naohiro Nomoto_, Mar 14 2004