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A369652
Maximal digit in the primorial base representation of the n-th arithmetic derivative of 128.
1
4, 4, 6, 2, 6, 11, 8, 7, 11, 11, 8, 10, 15, 15, 12, 18, 17, 30, 28, 22, 21, 37, 28, 38, 42, 33, 22, 52, 43, 56, 47, 49, 57, 60, 55, 54, 58, 70, 52, 66, 68, 57, 63, 86, 58, 88, 92, 66, 78, 95, 85, 52, 102, 70, 111, 57, 117, 99, 136, 104, 129, 110, 146, 127, 135, 132, 131, 129, 126, 145, 112, 150, 128, 129, 154, 161, 145
OFFSET
0,1
COMMENTS
This sequence relates to the question whether A327969(128) has a positive integer value, or whether it is -1 by the escape clause.
Note that when iterating the map k -> k' from A276086(A369638(4)) = A276086(15232) = 3299611946113357875 onward, the maximal exponent in the prime factorization (A051903) keeps on decreasing until it reaches 1 at the fifth iteration, and then stays as 1 for three more iterations (with k then 38863666759992439 = 643*60441161368573), but then, alas, on the next iteration, k' = 60441161369216 = 2^7 * 472196573197.
FORMULA
a(n) = A328114(A369638(n)).
EXAMPLE
The third arithmetic derivative (A099306) of 128 is 5056, which in primorial base (A049345) is written as 220220, therefore a(3) = 2.
The fourth arithmetic derivative (A258644) of 128 is 15232, which in primorial base is written as 663320, therefore a(4) = 6.
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 04 2024
STATUS
approved