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

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..30030

Index entries for sequences related to primorial base

Formula

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

Example

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).

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 *)

Prog

(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))))))

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.

Sequence in context: A099563 A099564 A341356 * A341348 A194606 A331180

Adjacent sequences: A276150 A276151 A276152 * A276154 A276155 A276156

Keyword

nonn,base

Author

Antti Karttunen, Aug 22 2016

Status

approved