

A284798


Antipalindromic numbers in base 3.


1



1, 4, 6, 13, 21, 34, 40, 46, 60, 66, 72, 97, 121, 145, 177, 201, 225, 268, 286, 304, 346, 364, 382, 424, 442, 460, 510, 528, 546, 588, 606, 624, 666, 684, 702, 781, 853, 925, 1021, 1093, 1165, 1261, 1333, 1405, 1509, 1581, 1653, 1749, 1821, 1893, 1989, 2061, 2133
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OFFSET

1,2


COMMENTS

Fixed points of the transform A284797.
A badic "antipalindrome" is a string of digits x where the application of the map d > b1d to each digit, followed by reversal of all digits, is equal to x. This sequence lists the integers whose base3 representation (with no leading zeros) has this property.


LINKS

Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv preprint arXiv:2008.06864 [math.CO], August 16 2020.


EXAMPLE

34 is a term of the sequence because 34 in base 3 is 1021, its digitbydigit complement in base 3 is 1201 and the digit reverse is again 1021.


MAPLE

P:=proc(q, h) local a, b, k, n; for n from 1 to q do a:=convert(n, base, h); b:=0;
for k from 1 to nops(a) do a[k]:=h1a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2, 8);


PROG

(Python)
from itertools import count, islice
from gmpy2 import digits
def A284798_gen(): return (n for n in count(0) if not n+int((s:=digits(n, 3)[::1]), 3)+13**len(s))


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



EXTENSIONS



STATUS

approved



