

A296130


Replace each digit of n with its complement to 9; this will reproduce all digits of n in a different order.


1



18, 27, 36, 45, 54, 63, 72, 81, 90, 1089, 1098, 1188, 1278, 1287, 1368, 1386, 1458, 1485, 1548, 1584, 1638, 1683, 1728, 1782, 1809, 1818, 1827, 1836, 1845, 1854, 1863, 1872, 1881, 1890, 1908, 1980, 2079, 2097, 2178, 2187, 2277, 2367, 2376, 2457, 2475, 2547, 2574, 2637, 2673, 2709, 2718
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OFFSET

1,1


COMMENTS

The complement of 0 is 9, of 1 is 8, of 2 is 7, etc. All terms of the sequence have an even number of digits, and all terms are divisible by 9.


LINKS



EXAMPLE

18 produces 81 when 1 is replaced by 8 and 8 is replaced by 1; 18 and 81 use the same set of digits, in a different order.
1089 produces 8910 when 1 is replaced by 8, 0 by 9, 8 by 1 and 9 by 0; 1089 and 8910 use the same set of digits, in a different order.


PROG

(PARI) replace_digits(n) = my(d=digits(n)); for(k=1, #d, d[k]=abs(d[k]9)); d
is(n) = vecsort(digits(n))==vecsort(replace_digits(n)) \\ Felix Fröhlich, Feb 14 2018


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



