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

1,1

Comments

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

Links

Table of n, a(n) for n=1..32.

Example

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.

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

Prog

(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 n<x+y else (c:=n-y)*y+int(str(c)[::-1] or 0)
    for n in count(max(2, startvalue)):
        if str(n) in str(k:=f(n)):
            yield k
A248753_list = list(islice(A248753_gen(), 32)) # Chai Wah Wu, Jul 24 2024

Crossrefs

Cf. A002113, A248754.

Sequence in context: A290067 A289934 A289968 * A248754 A099814 A340549

Adjacent sequences: A248750 A248751 A248752 * A248754 A248755 A248756

Keyword

nonn,base,easy

Author

Robert G. Wilson v, Oct 13 2014

Status

approved