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

1,2

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

Table of n, a(n) for n=1..53.

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

Cf. A035928, A284797.

Sequence in context: A007977 A013122 A012964 * A120463 A049732 A262194

Adjacent sequences: A284795 A284796 A284797 * A284799 A284800 A284801

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 03 2017

Extensions

New name from Jeffrey Shallit, Nov 04 2023

Status

approved