A276153 The most significant digit when n is written in primorial base (A049345).

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, 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, 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

Offset: 0

Author

Antti Karttunen, Aug 22 2016

Keywords

• nonn
• base

Examples

			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.
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.
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).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial base

Crossrefs

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

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

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

Programs

Mathematica

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

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))))))

Formula

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