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A328114
Maximal digit value used when n is written in primorial base (cf. A049345).
54
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 12 2019
STATUS
approved