%I #25 Mar 11 2021 21:07:13

%S 0,1,1,1,2,2,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N The most significant digit in A097801-base.

%C 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. Therefore this sequence differs from A276153 for the first time at n=1890, where a(1890)=1, while A276153(1890)=9, as 1890 = 9*A002110(4).

%C Therefore this sequence might be produced as a rough approximation of A276153 by naive machine learning/mining algorithms. - _Antti Karttunen_, Mar 09 2021

%H Antti Karttunen, <a href="/A341356/b341356.txt">Table of n, a(n) for n = 0..65537</a>

%e 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. In the same base, number 30 is expressed as "1000" as 30 = 1*30, thus a(30) = 1.

%e Number 1890 = 2*3*5*7*9 is expressed as "100000", thus a(1890) = 1.

%t Block[{nn = 105, b}, b = MixedRadix@ NestWhile[Prepend[#1, 2 #2 - 1] & @@ {#, Length[#] + 1} &, {2}, Times @@ # < nn &]; Array[First@ IntegerDigits[#, b] &, nn + 1, 0]] (* _Michael De Vlieger_, Feb 23 2021 *)

%o (PARI) A341356(n) = { my(m=2, k=3); while(n>=m, n \= m; m = k; k += 2); (n); }; \\ _Antti Karttunen_ & _Kevin Ryde_, Feb 24 2021

%Y Cf. A097801.

%Y Cf. A341513 (sum of digits in the same base), A341514 (number of trailing zeros).

%Y Cf. also A002110, A049345.

%Y Differs from similarly constructed A276153 for the first time at n=1890, where a(1890)=1, while A276153(1890)=9.

%Y Differs from similarly constructed A099564 for the first time at n=210, where a(210)=1, while A099564(210)=7.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Feb 23 2021