A284811 Fixed points of the transform A267193.

18, 27, 36, 45, 54, 63, 72, 81, 90, 1098, 1188, 1278, 1368, 1458, 1548, 1638, 1728, 1818, 1908, 2097, 2187, 2277, 2367, 2457, 2547, 2637, 2727, 2817, 2907, 3096, 3186, 3276, 3366, 3456, 3546, 3636, 3726, 3816, 3906, 4095, 4185, 4275, 4365, 4455, 4545, 4635, 4725

Offset: 1

Author

Paolo P. Lava, Apr 05 2017

Keywords

• nonn
• base
• easy

Comments

These numbers are called antipalindromic in base 10 by Dvorakova et al. - Michel Marcus, Aug 18 2020

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..9999
• Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv:2008.06864 [math.CO], 2020.

Crossrefs

Cf. A035928, A061601, A267193.

Subsequence of A008591 (multiples of 9).

Programs

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(10^2,10);

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

PARI

a(n) = my (d=digits(n)); n*10^#d + fromdigits(apply (t -> 9-t, Vecrev(d))) \\ Rémy Sigrist, Aug 18 2020