A341356 The most significant digit in A097801-base.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Feb 23 2021

Keywords

• nonn
• base

Comments

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).

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

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A097801.

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

Cf. also A002110, A049345.

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

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

Programs

Mathematica

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 *)

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