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A341356
The most significant digit in A097801-base.
3
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
0,5
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
LINKS
EXAMPLE
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.
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 *)
PROG
(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
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.
Sequence in context: A337198 A099563 A099564 * A276153 A341348 A194606
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Feb 23 2021
STATUS
approved