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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Fixed points of the transform A284797.
A b-adic "antipalindrome" is a string of digits x where the application of the map d -> b-1-d to each digit, followed by reversal of all digits, is equal to x. This sequence lists the integers whose base-3 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 digit-by-digit 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]:=h-1-a[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)+1-3**len(s))
A284798_list = list(islice(A284798_gen(), 35)) # Chai Wah Wu, Feb 04 2022
CROSSREFS
Sequence in context: A007977 A013122 A012964 * A120463 A049732 A262194
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Apr 03 2017
EXTENSIONS
New name from Jeffrey Shallit, Nov 04 2023
STATUS
approved

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Last modified December 6 16:13 EST 2023. Contains 367612 sequences. (Running on oeis4.)