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
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.
Programs
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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
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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
Comments