A109625 Numbers k such that concatenation of k and its 10's complement is a palindrome.

5, 91, 9091, 9181, 9271, 9361, 9451, 9541, 9631, 9721, 9811, 900991, 901891, 902791, 903691, 904591, 905491, 906391, 907291, 908191, 909091, 910981, 911881, 912781, 913681, 914581, 915481, 916381, 917281, 918181, 919081, 920971, 921871, 922771

Offset

1,1

Comments

For n > 1, numbers with digits x_1 ... x_{2*k} where x_1 = 9, x_{2*k} = 1, x_2 <= 8 and

x_{2k-i} + x_{i+1} = 9 for 2 <= i <= 2k-1. - Robert Israel, May 17 2026

Links

Robert Israel, Table of n, a(n) for n = 1..10001

Example

a(3)=9091 because 10^4-9091 = 909 and concatenating produces the palindrome
9091909.

Maple

f:= proc(x) local i, L;
    L:= convert(x, base, 10);
    10^nops(L)*x + add((9-L[-i])*10^(i-1), i=1..nops(L))+1;
end proc:
[5, 91, seq(seq(f(9*10^d+j), j=0..9*10^(d-1)-1), d=1..3)]; # Robert Israel, May 17 2026

Mathematica

Select[Range[923000], PalindromeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[ 10^IntegerLength[ #]-#]]]]&] (* Harvey P. Dale, Nov 01 2022 *)

Crossrefs

Sequence in context: A340052 A392486 A340883 * A266290 A348347 A222903

Adjacent sequences: A109622 A109623 A109624 * A109626 A109627 A109628

Keyword

base,nonn

Author

Jason Earls, Aug 02 2005

Status

approved