A248754 Palindromes p=A002113(n) whose index n is also a palindrome and in addition a substring of p (strings in base 10).

11, 1111, 12221, 23332, 34443, 45554, 56665, 67776, 78887, 89998, 111111, 1222221, 2333332, 3444443, 4555554, 5666665, 6777776, 7888887, 8999998, 9101019, 11111111, 102020201, 112121211, 122222221, 132323231, 142424241, 152525251, 162626261, 172727271, 182828281

Offset: 1

Author

Robert G. Wilson v, Oct 13 2014

Keywords

• nonn
• base
• easy

Comments

This is a proper subsequence of A248753 (where the index does not need to be palindromic).

Examples

			11 is a term because the eleventh palindrome is 11.
1111 is a member because it is the 111th palindrome.
12221 is in the sequence because the 222nd palindrome is 12221.
		

Crossrefs

Cf. A002113, A248753.

Programs

Mathematica

(* first load 'nthPalindrome' from A002113 and then *) nPal[n_] := nthPalindrome[n - 1];  fQ[n_] := StringPosition[ ToString[ nPal[ nPal[ k]]], ToString[ nPal[ n]]] != {}; k = 2; lst = {}; While[k < 501, If[ fQ[k], AppendTo[lst, nPal[ nPal[ k]] ]]; k++]; lst

Python

from itertools import count, islice
def A248754_gen(): # generator of terms
    def f(n):
        y = 10*(x:=10**(len(str(n>>1))-1))
        return (c:=n-x)*x+int(str(c)[-2::-1] or 0) if nA248754_list = list(islice(A248754_gen(),30)) # Chai Wah Wu, Jul 24 2024