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Fixed points of the transform A267193.
2

%I #21 Aug 19 2020 16:04:14

%S 18,27,36,45,54,63,72,81,90,1098,1188,1278,1368,1458,1548,1638,1728,

%T 1818,1908,2097,2187,2277,2367,2457,2547,2637,2727,2817,2907,3096,

%U 3186,3276,3366,3456,3546,3636,3726,3816,3906,4095,4185,4275,4365,4455,4545,4635,4725

%N Fixed points of the transform A267193.

%C These numbers are called antipalindromic in base 10 by Dvorakova et al. - _Michel Marcus_, Aug 18 2020

%H Rémy Sigrist, <a href="/A284811/b284811.txt">Table of n, a(n) for n = 1..9999</a>

%H Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, <a href="https://arxiv.org/abs/2008.06864">Antipalindromic numbers</a>, arXiv:2008.06864 [math.CO], 2020.

%e 1278 is a term of the sequence because its complement in base 10 is 8721 and the digit reversal is again 1278.

%p P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;

%p 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(10^2,10);

%o (PARI) isok(m) = {my(d=digits(m)); for (j=1, #d, if (d[j] + d[#d+1-j] != 9, return(0));); return (1);} \\ _Michel Marcus_, Aug 18 2020

%o (PARI) a(n) = my (d=digits(n)); n*10^#d + fromdigits(apply (t -> 9-t, Vecrev(d))) \\ _Rémy Sigrist_, Aug 18 2020

%Y Cf. A035928, A061601, A267193.

%Y Subsequence of A008591 (multiples of 9).

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Apr 05 2017