A351089 - OEIS

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.

-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

(list; graph; refs; listen; history; text; internal format)

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