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

%I A328114 #23 Oct 30 2019 22:07:09
%S A328114 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,
%T A328114 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,
%U A328114 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
%N A328114 Maximal digit value used when n is written in primorial base (cf. A049345).
%H A328114 Antti Karttunen, <a href="/A328114/b328114.txt">Table of n, a(n) for n = 0..30030</a>
%H A328114 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328114 a(n) = A051903(A276086(n)).
%F A328114 a(A276156(n)) = 1 for all n >= 1.
%F A328114 a(n) <= A276150(n) for all n >= 0.
%F A328114 From _Antti Karttunen_, Oct 29 2019: (Start)
%F A328114 a(n) = A061395(A328835(n)).
%F A328114 For n >= 1, a(n) < A000040(A235224(n)) and a(n) <= 1 + A328391(n).
%F A328114 For all n >= 1, a(n) = 1+A051903(A328572(n)).
%F A328114 a(A276086(n)) = A328389(n), a(A276087(n)) = A328394(n), a(A328403(n)) = A328398(n).
%F A328114 a(A327860(n)) = A328392(n), a(A003415(n)) = A328390(n), a(A328316(n)) = A328322(n).
%F A328114 (End)
%e A328114 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.
%t A328114 With[{b = MixedRadix[Reverse@ Prime@ Range@ 20]}, Array[Max@ IntegerDigits[#, b] &, 105, 0]] (* _Michael De Vlieger_, Oct 30 2019 *)
%o A328114 (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); };
%o A328114 (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
%Y A328114 Cf. A002110, A049345, A051903, A061395, A276086, A267263, A276150, A327969, A328316, A328322, A328389, A328390, A328392, A328394, A328398, A328403, A328835.
%Y A328114 Cf. A276156 (indices of terms < 2).
%K A328114 nonn
%O A328114 0,5
%A A328114 _Antti Karttunen_, Oct 12 2019