A055198 Numbers n with property that n cycles to itself after sufficiently many iterations of "reverse decimal digits of (n+4)".

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

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

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