A369652 Maximal digit in the primorial base representation of the n-th arithmetic derivative of 128.

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

Author

Antti Karttunen, Feb 04 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..142
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A049345, A099306, A258644, A328114, A369638.

Cf. also A327969.

Formula

a(n) = A328114(A369638(n)).