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A341513 Sum of digits in A097801-base.

%I A341513 #13 Feb 24 2021 08:18:56
%S A341513 0,1,1,2,2,3,1,2,2,3,3,4,2,3,3,4,4,5,3,4,4,5,5,6,4,5,5,6,6,7,1,2,2,3,
%T A341513 3,4,2,3,3,4,4,5,3,4,4,5,5,6,4,5,5,6,6,7,5,6,6,7,7,8,2,3,3,4,4,5,3,4,
%U A341513 4,5,5,6,4,5,5,6,6,7,5,6,6,7,7,8,6,7,7,8,8,9,3,4,4,5,5,6,4,5,5,6,6,7,5,6,6,7
%N A341513 Sum of digits in A097801-base.
%C A341513 A097801-base uses values 1, 2, 2*3, 2*3*5, 2*3*5*7, 2*3*5*7*9, 2*3*5*7*9*11, 2*3*5*7*9*11*13, 2*3*5*7*9*11*13*15, ..., for its digit-positions, instead of primorials (A002110), thus up to 1889 = 2*3*5*7*9 - 1 = 9*A002110(4) - 1 its representation is identical with the primorial base A049345. Thus this sequence differs from A276150 for the first time at n=1890, where a(1890)=1, while A276150(1890)=9, as 1890 = 9*A002110(4).
%H A341513 Antti Karttunen, <a href="/A341513/b341513.txt">Table of n, a(n) for n = 0..65537</a>
%e A341513 In A097801-base, where the digit-positions are given by 1 and the terms of A097801 from its term a(1) onward: 2, 6, 30, 210, 1890, 20790, 270270, 4054050, ..., number 29 is expressed as "421" as 29 = 4*6 + 2*2 + 1*1, thus a(29) = 4+2+1 = 7. In the same base, number 30 is expressed as "1000" as 30 = 1*30, thus a(30) = 1, and number 1890 = 2*3*5*7*9 is expressed as "100000", thus a(1890) = 1 also.
%t A341513 Block[{nn = 105, b}, b = MixedRadix@ NestWhile[Prepend[#1, 2 #2 - 1] & @@ {#, Length[#] + 1} &, {2}, Times @@ # < nn &]; Array[Total@ IntegerDigits[#, b] &, nn + 1, 0]] (* _Michael De Vlieger_, Feb 23 2021 *)
%o A341513 (PARI) A341513(n) = { my(u=0,m=2,k=3); while(n, u += n%m; n \= m; m = k; k += 2); (u); };
%Y A341513 Cf. A097801, A341356 (most significant digit in the same base).
%Y A341513 Cf. also A002110, A049345, A276150.
%K A341513 nonn,base
%O A341513 0,4
%A A341513 _Antti Karttunen_, Feb 23 2021