A248753 Palindromes p = A002113(n) whose index n is a substring of p.

11, 1111, 12221, 23332, 34443, 45554, 56665, 67776, 78887, 89998, 101101, 111111, 121121, 131131, 141141, 151151, 161161, 171171, 181181, 191191, 1020201, 1121211, 1222221, 1323231, 1424241, 1525251, 1626261, 1727271, 1828281, 1929291, 2030302, 2131312

Offset: 1

Author

Robert G. Wilson v, Oct 13 2014

Keywords

• nonn
• base
• easy

Comments

That is to say the 'n' of A002113(n) is a substring of A002113(n).

Examples

			11 is a term because the eleventh palindrome is 11.
12221 is in the sequence because the 222nd palindrome is 12221.
101101 is a member because it is the 1101st palindrome.
		

Crossrefs

Cf. A002113, A248754.

Programs

Mathematica

(* first load 'nthPalindrome' from A002113 and then *) nPal[n_] := nthPalindrome[n - 1]; fQ[n_] := StringPosition[ ToString[ nPal[ n]], ToString[ n]] != {}; k = 1; lst = {}; While[k < 3001, If[fQ[k], AppendTo[lst, nPal[ k]]]; k++]; lst

Python

from itertools import count, islice
def A248753_gen(startvalue=2): # generator of terms >= startvalue
    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 nA248753_list = list(islice(A248753_gen(),32)) # Chai Wah Wu, Jul 24 2024