OFFSET
1,6
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.
From Amiram Eldar, Mar 10 2021: (Start)
The asymptotic density of the occurrences of k is 1/2 if k=0, and 2*k/(A097801(k+1)) otherwise.
The asymptotic mean of this sequence is sqrt(e*Pi/2)*erf(1/sqrt(2))/2 = 0.7053430673..., where erf(x) is the error function. (End)
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
For odd n, a(n) = 0; for even n, a(n) = the largest k such that A097801(k) divides n.
EXAMPLE
In A097801-base number 1890 = 2*3*5*7*9 is expressed as "100000", thus a(1890) = 5.
MATHEMATICA
Block[{nn = 105, b}, b = MixedRadix@ NestWhile[Prepend[#1, 2 #2 - 1] & @@ {#, Length[#] + 1} &, {2}, Times @@ # < nn &]; Array[LengthWhile[Reverse@ IntegerDigits[#, b], # == 0 &] &, nn]] (* Michael De Vlieger, Feb 25 2021 *)
PROG
(PARI) A341514(n) = { my(m=2, k=3, i=0); while(!(n%m), n /= m; m = k; k += 2; i++); (i); };
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Feb 25 2021
STATUS
approved