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

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

Example

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.

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

Prog

(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 n<x+y else (c:=n-y)*y+int(str(c)[::-1] or 0)
    for n in count(2):
        if str(m:=f(n)) in str(k:=f(m)):
            yield k
A248754_list = list(islice(A248754_gen(), 30)) # Chai Wah Wu, Jul 24 2024

Crossrefs

Cf. A002113, A248753.

Sequence in context: A289934 A289968 A248753 * A099814 A340549 A260077

Adjacent sequences: A248751 A248752 A248753 * A248755 A248756 A248757

Keyword

nonn,base,easy

Author

Robert G. Wilson v, Oct 13 2014

Status

approved