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.

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, 21, 23, 24, 27, 27, 27, 29, 29, 32, 29, 35, 33, 36, 32, 38, 37, 41, 39, 41, 40, 42, 41, 45, 43, 45, 46, 48, 47, 49, 50, 52, 52, 55, 53, 57, 58, 56, 57, 59, 60, 61

Offset: 0

Author

Naohiro Nomoto, Mar 14 2004

Keywords

• nonn
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Density plot of (n, R_k(n)) for n = 0..1000 and k >= 2

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963, A181385.

Programs

Mathematica

rev[x_, b_]:=FromDigits[Reverse[IntegerDigits[x, b]], b]
Length /@ Union /@ Table[Table[rev[x, b], {b, 2, x + 1}], {x, 1, 200}] (* Dylan Hamilton, Oct 16 2010 *)

PARI

a(n) = #Set(apply(b -> fromdigits(Vecrev(digits(n,b)),b), [2..max(2,n+1)])) \\ Rémy Sigrist, Jan 29 2020