OFFSET
1,2
COMMENTS
A regular pattern of rectangles, each 10 times larger than the last, appears on the scatter plot of this sequence. However, there are moments where the sequence deviates from its current rectangle to drop down to lower orders of magnitude or jump up to higher ones. Additionally, chaotic behavior can be observed at values of n in the approximate intervals [60000, 63000], [68000, 82000], and [85000, 100000].
Not all integers appear in this sequence. The smallest number that will never occur is 130, as the only way to achieve the number is through 129, which had already been used to jump to 921.
LINKS
Sylvia Zevi Abrams, Table of n, a(n) for n = 1..10000 [Corrected to remove leading 0's by Sean A. Irvine]
Sylvia Zevi Abrams, Scatter Plot, for n < 100000
EXAMPLE
a(11) = 11 because R(a(10)) = 1, which was already used as a(1).
a(13) = 21 because R(a(12)) = 21, which had not yet been used, and a(11) =! R(a(12)).
a(64) = 20 because although R(a(63)) = 91 and 91 has not yet been used, a(63) = R(a(62)).
PROG
(PARI) R(n) = fromdigits(Vecrev(digits(n))); \\ A004086
leastunused(va, m) = my(k=va[m]+1); while (#select(x->(x==k), va), k++); k;
lista(nn) = my(va = vector(nn)); va[1] = 1; va[2] = 2; for (n=3, nn, if ((va[n-1] != R(va[n-2])) && !#select(x->(x==R(va[n-1])), va), va[n] = R(va[n-1]), va[n] = leastunused(va, n-1)); ); va; \\ Michel Marcus, Jul 12 2022
CROSSREFS
KEYWORD
AUTHOR
Sylvia Zevi Abrams, Jul 09 2022
STATUS
approved