

A351089


Number of iterations of map x > A003415(x) needed to reach a number >= A276086(n), when starting from x = n, or 1 if such number is never reached.


7



1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 6, 4, 1, 1, 1, 6, 1, 1, 1, 6, 1, 11, 1, 8, 1, 0, 0, 0, 1, 1, 5, 0, 1, 1, 5, 7, 1, 1, 1, 4, 8, 1, 1, 4, 1, 10, 10, 8, 1, 7, 10, 8, 1, 1, 1, 0, 1, 1, 8, 2, 1, 1, 1, 6, 11, 1, 1, 6, 1, 10, 10, 8, 1, 1, 1, 7, 9, 1, 1, 7, 1, 14, 11, 9
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OFFSET

0,9


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to primorial base


EXAMPLE

a(0) = 1 because A003415^(k)(0) = 0 for all values of k >= 0 (i.e., regardless of how many times we apply the arithmetic derivative), and 0 < A276086(0) = 1.
a(1) = 1 because A003415^(k)(1) = 0 for all values of k >= 1, and both 1 and 0 are less than A276086(1) = 2.
a(4) = 1 because A003415^(k)(4) = 4 for all values of k >= 0 (i.e., regardless of how many times we apply the arithmetic derivative), and 4 < A276086(4) = 9.
a(6) = 0 because 6 is already >= A276086(6) = 5 before any iterations.
a(8) = 2 because it takes two iterations with A003415 as 8 > 12 > 16 to obtain a number >= A276086(8) = 15.


PROG

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351089(n) = { my(u=A276086(n), i=0, prev_n=1); while(n>0, if(n>=u, return(i)); prev_n = n; n = A003415(n); if(n==prev_n, return(1)); i++); (1); };


CROSSREFS

Cf. A003415, A276086, A349908 (positions of records), A351226 (positions of zeros), A351229 (positions of ones).
Cf. also A351088.
Sequence in context: A055652 A290084 A154844 * A133831 A325613 A305054
Adjacent sequences: A351086 A351087 A351088 * A351090 A351091 A351092


KEYWORD

sign,base,look


AUTHOR

Antti Karttunen, Feb 05 2022


STATUS

approved



