A045571 Numbers that are palindromic, divisible by 11 and have an odd number of digits.

121, 242, 363, 484, 616, 737, 858, 979, 10901, 11011, 12221, 13431, 14641, 15851, 17171, 18381, 19591, 20702, 21912, 22022, 23232, 24442, 25652, 26862, 28182, 29392, 30503, 31713, 32923, 33033, 34243, 35453, 36663, 37873, 39193, 40304

Offset

1,1

Comments

All the palindromic numbers with an even number of digits are divisible by 11. The number of palindromic numbers with 2*k+1 digits that are divisible by 11 is (10^(k+1) + (-1)^k)/11, and their asymptotic relative density within the set of all palindromic numbers with an odd number of digits (A056525) is 1/11 (Schmidt, 1988). - Amiram Eldar, Jan 11 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Harvey Schmidt, Jr., Palindromes: Density and Divisibility, Mathematics Magazine, Vol. 61, No. 5 (1988), pp. 297-300.

Mathematica

Select[11 * Range[4000], PalindromeQ[#] && OddQ[IntegerLength[#]] &] (* Amiram Eldar, Jan 11 2021 *)

Crossrefs

Intersection of A056525 and A083852.

Sequence in context: A084998 A082944 A131973 * A088285 A218172 A083749

Adjacent sequences: A045568 A045569 A045570 * A045572 A045573 A045574

Keyword

base,nonn

Author

Jeff Burch

Status

approved