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

1,1

Comments

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

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.

Example

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

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);

Prog

(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

Crossrefs

Cf. A035928, A061601, A267193.

Subsequence of A008591 (multiples of 9).

Sequence in context: A262277 A144777 A296130 * A257001 A367341 A109911

Adjacent sequences: A284808 A284809 A284810 * A284812 A284813 A284814

Keyword

nonn,base,easy

Author

Paolo P. Lava, Apr 05 2017

Status

approved