

A055198


Numbers n with property that n cycles to itself after sufficiently many iterations of "reverse decimal digits of (n+4)".


5



1, 2, 5, 6, 9, 13, 16, 24, 27, 31, 35, 38, 53, 57, 68, 71, 75, 79, 82, 93, 97, 101, 122, 137, 141, 177, 181, 217, 304, 319, 323, 359, 363, 399, 501, 505, 526, 541, 545, 581, 585, 621, 708, 723, 727, 763, 767, 803, 905, 909, 945, 949, 985, 989, 1011, 1013, 1015
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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 length90 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 5digit terms. Looking through 6digit integers one finds that, in addition to the abovementioned 22 length1890 cycles, there are 449 length450 cycles (224 odd starting integers from 100101 to 100547, 113 alternateodd starting integers from 100551 to 100999, and 112 alternateodd starting integers from 110111 to 110555) and 2 length225 cycles (for starting integers 100549 and 110559). Added to the existing 2034term bfile 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 BrÃ¶mssen, Mar 19 2022


CROSSREFS

Cf. A003608, A016081, A016082, A119031.
Sequence in context: A094350 A104857 A285899 * A103982 A030488 A190678
Adjacent sequences: A055195 A055196 A055197 * A055199 A055200 A055201


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



