A284798 Antipalindromic numbers in base 3.
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
Offset: 1
Examples
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.
Links
- Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv preprint arXiv:2008.06864 [math.CO], August 16 2020.
Programs
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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);
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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)) A284798_list = list(islice(A284798_gen(),35)) # Chai Wah Wu, Feb 04 2022
Extensions
New name from Jeffrey Shallit, Nov 04 2023
Comments