A276153 - OEIS

%I #14 Aug 31 2016 20:54:03

%S 0,1,1,1,2,2,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4

%N The most significant digit when n is written in primorial base (A049345).

%H Antti Karttunen, <a href="/A276153/b276153.txt">Table of n, a(n) for n = 0..30030</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A071178(A276086(n)).

%e For n=24, which is "400" in primorial base (as 24 = 4*(3*2*1) + 0*(2*1) + 0*1, see A049345), the most significant digit is 4, thus a(24) = 4.

%e For n=210, which is "10000" in primorial base (as 210 = A002110(4) = 7*5*3*2*1), the most significant digit is 1, thus a(210) = 1.

%e For n=2100, which could be written "A0000" in primorial base (where A stands for digit "ten", as 2100 = 10*A002110(4)), the most significant value holder is thus 10 and a(2100) = 10. (The first point where this sequence attains a value larger than 9).

%t nn = 120; Table[First@ IntegerDigits[n, MixedRadix[Reverse@ Prime@ Range@ PrimePi@ nn]], {n, 0, nn}] (* _Michael De Vlieger_, Aug 25 2016, Version 10.2 *)

%o (Scheme) (define (A276153 n) (let loop ((n n) (i 1)) (let* ((p (A000040 i)) (dig (modulo n p)) (next-n (/ (- n dig) p))) (if (zero? next-n) dig (loop next-n (+ 1 i))))))

%Y Cf. A000040, A002110, A049345, A071178, A276086.

%Y Differs from A099563 for the first time at n=24.

%Y Differs from A099564 for the first time at n=210, where a(210)=1, while A099564(210)=7.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Aug 22 2016