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

Author

Jeff Burch

Keywords

• base
• nonn

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.

Crossrefs

Intersection of A056525 and A083852.

Programs

Mathematica

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