cp's OEIS Frontend

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

%I A248753 #13 Jul 24 2024 18:10:53
%S A248753 11,1111,12221,23332,34443,45554,56665,67776,78887,89998,101101,
%T A248753 111111,121121,131131,141141,151151,161161,171171,181181,191191,
%U A248753 1020201,1121211,1222221,1323231,1424241,1525251,1626261,1727271,1828281,1929291,2030302,2131312
%N A248753 Palindromes p = A002113(n) whose index n is a substring of p.
%C A248753 That is to say the 'n' of A002113(n) is a substring of A002113(n).
%e A248753 11 is a term because the eleventh palindrome is 11.
%e A248753 12221 is in the sequence because the 222nd palindrome is 12221.
%e A248753 101101 is a member because it is the 1101st palindrome.
%t A248753 (* 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
%o A248753 (Python)
%o A248753 from itertools import count, islice
%o A248753 def A248753_gen(startvalue=2): # generator of terms >= startvalue
%o A248753     def f(n):
%o A248753         y = 10*(x:=10**(len(str(n>>1))-1))
%o A248753         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)
%o A248753     for n in count(max(2,startvalue)):
%o A248753         if str(n) in str(k:=f(n)):
%o A248753             yield k
%o A248753 A248753_list = list(islice(A248753_gen(),32)) # _Chai Wah Wu_, Jul 24 2024
%Y A248753 Cf. A002113, A248754.
%K A248753 nonn,base,easy
%O A248753 1,1
%A A248753 _Robert G. Wilson v_, Oct 13 2014