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Leading digit of n in base 6.
3

%I #15 Dec 22 2024 14:28:43

%S 1,2,3,4,5,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,

%T 5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2

%N Leading digit of n in base 6.

%H Kevin Ryde, <a href="/A339256/b339256.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n / 6^floor(log_6(n))).

%F G.f.: (x + Sum_{k>=0} Sum_{d=2..5} (x^(d*6^k)-x^(6^(k+1))) )/(1-x).

%t Table[IntegerDigits[n,6][[1]],{n,90}] (* _Harvey P. Dale_, Jul 19 2023 *)

%o (PARI) a(n) = n\6^logint(n,6);

%Y Cf. A007092 (base 6), A109804 (partial sums).

%Y In other bases: A122586, A122587, A339255, A000030, A099563, A276153.

%K base,nonn

%O 1,2

%A _Kevin Ryde_, Nov 28 2020