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

0,5

Links

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

Index entries for sequences related to primorial base

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)

Example

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.

Mathematica

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

Prog

(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

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).

Sequence in context: A157129 A101615 A246359 * A343504 A328582 A227153

Adjacent sequences: A328111 A328112 A328113 * A328115 A328116 A328117

Keyword

nonn

Author

Antti Karttunen, Oct 12 2019

Status

approved