A328114 Maximal digit value used when n is written in primorial base (cf. A049345).

0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Antti Karttunen, Oct 12 2019

Keywords

• nonn

Examples

			For n = 2105, which could be expressed in primorial base for example as "T0021" (where T here stands for the digit value ten), or maybe more elegantly as [10,0,0,2,1] as 2105 = 10*A002110(4) + 2*A002110(1) + 1*A002110(0). The maximum value of these digits is 10, thus a(2105) = 10.
		

Links

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

Crossrefs

Cf. A002110, A049345, A051903, A061395, A276086, A267263, A276150, A327969, A328316, A328322, A328389, A328390, A328392, A328394, A328398, A328403, A328835.

Cf. A276156 (indices of terms < 2).

Programs

Mathematica

With[{b = MixedRadix[Reverse@ Prime@ Range@ 20]}, Array[Max@ IntegerDigits[#, b] &, 105, 0]] (* Michael De Vlieger, Oct 30 2019 *)

PARI

A328114(n) = { my(i=0,m=0,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m = max(m,(n%nextpr)/pr); n-=(n%nextpr));pr=nextpr); (m); };

PARI

A328114(n) = { my(s=0, p=2); while(n, s = max(s,(n%p)); n = n\p; p = nextprime(1+p)); (s); }; \\ (Faster, no unnecessary construction of primorials) - Antti Karttunen, Oct 29 2019

Formula

a(n) = A051903(A276086(n)).

a(A276156(n)) = 1 for all n >= 1.

a(n) <= A276150(n) for all n >= 0.

From Antti Karttunen, Oct 29 2019: (Start)

a(n) = A061395(A328835(n)).

For n >= 1, a(n) < A000040(A235224(n)) and a(n) <= 1 + A328391(n).

For all n >= 1, a(n) = 1+A051903(A328572(n)).

a(A276086(n)) = A328389(n), a(A276087(n)) = A328394(n), a(A328403(n)) = A328398(n).

a(A327860(n)) = A328392(n), a(A003415(n)) = A328390(n), a(A328316(n)) = A328322(n).

(End)