OFFSET
1,2
COMMENTS
Sean A. Irvine noted on Mar 14, 2022, that the sequence had more than the previously described 54 terms less than 1000. Specifically, the combined and sorted 22 length-90 iterations for odd starting integers from 1011 to 1053 follow. In fact, it appears that the 22 length-[2*10^(n+1)-110] iterations for odd starting integers from 10^(2*n+1)+11 to 10^(2*n+1)+53 are, for positive n, all terms. - Hans Havermann, Mar 18 2022
There are no 5-digit terms. Looking through 6-digit integers one finds that, in addition to the above-mentioned 22 length-1890 cycles, there are 449 length-450 cycles (224 odd starting integers from 100101 to 100547, 113 alternate-odd starting integers from 100551 to 100999, and 112 alternate-odd starting integers from 110111 to 110555) and 2 length-225 cycles (for starting integers 100549 and 110559). Added to the existing 2034-term b-file makes for 246114 terms less than one million. Beyond one million one must contend with potentially long runs before entering a cycle. For example, 1001011 requires 25037505 iterations to reach the term 100021. - Hans Havermann, Apr 08 2022
REFERENCES
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 15.
LINKS
Hans Havermann, Table of n, a(n) for n = 1..2034
PROG
(Python)
from sympy import cycle_length
f=lambda x:int(''.join(reversed(str(x+4))))
def is_A055198(n):
return n in cycle_length(f, n, values=True)
print([n for n in range(1016) if is_A055198(n)]) # Pontus von Brömssen, Mar 19 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Henry Bottomley, Jun 30 2000
EXTENSIONS
Edited by N. J. A. Sloane, Aug 02 2009
Edited by Charles R Greathouse IV, Aug 04 2010
Deleted two versions of an incorrect conjecture. - N. J. A. Sloane, Mar 18 2022
Edited by Hans Havermann, Mar 18 2022
STATUS
approved