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A284798
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Antipalindromic numbers in base 3.
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2
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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
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1,2
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COMMENTS
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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.
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LINKS
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Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv preprint arXiv:2008.06864 [math.CO], August 16 2020.
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EXAMPLE
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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.
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MAPLE
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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);
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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