A341513 Sum of digits in A097801-base.

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, 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, 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

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. 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).

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+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.
		

Links

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

Crossrefs

Cf. A097801, A341356 (most significant digit in the same base).

Cf. also A002110, A049345, A276150.

Programs

Mathematica

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 *)

PARI

A341513(n) = { my(u=0,m=2,k=3); while(n, u += n%m; n \= m; m = k; k += 2); (u); };