This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
A128921(41) = 1119111, 1119111^2 = 1252409430321 is not a palindrome, but its reverse is also a square: 1230349042521 = 1109211^2.
b(n) = reverse of a(n). n | A128921(n) | a(n) | b(n) | Root of b(n) | --+------------+--------+--------+--------------+ 1 | 0 | 0 | 0 | 0 | 2 | 1 | 1 | 1 | 1 | 3 | 2 | 4 | 4 | 2 | 4 | 3 | 9 | 9 | 3 | 5 | 11 | 121 | 121 | 11 | 6 | 22 | 484 | 484 | 22 | 7 | 33 | 1089 | 9801 | 99 | 8 | 99 | 9801 | 1089 | 33 | 9 | 101 | 10201 | 10201 | 101 |
from itertools import count, chain, islice from sympy.ntheory.primetest import is_square def A319483_gen(): # generator of terms return filter(lambda n:is_square(int(str(n)[::-1])),map(lambda n: n**2, chain((0,),chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l,10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l,10**(l+1)))) for l in count(0))))) A319483_list = list(islice(A319483_gen(),20)) # Chai Wah Wu, Jun 23 2022
121 is OK since 121^2=14641 is also a palindrome.
dmax:= 7: # to get all terms with up to dmax digits
Res:= 0,1,2,3,11,22:
Po:= [[0],[1],[2],[3]]: Pe:= [[0,0],[1,1],[2,2]]:
for d from 1 to dmax do
if d::odd then
Po:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Po),i=0..2)]);
Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1),i=1..nops(p)) fi end proc, Po))
else
Pe:= select(t -> add(s^2,s=t) < 10, [seq(seq([i,op(t),i], t=Pe),i=0..2)]);
Res:= Res, op(map(proc(p) if p[1] <> 0 then add(p[i]*10^(i-1),i=1..nops(p)) fi end proc, Pe))
fi;
od:
Res; # Robert Israel, Jun 21 2017
PalQ[n_] := FromDigits[Reverse[IntegerDigits[n]]] == n; t = {}; Do[
If[PalQ[n] && PalQ[n^2], AppendTo[t, n]], {n, 0, 1200000}]; t (* Jayanta Basu, May 10 2013 *)
Select[Range[0,12*10^5],AllTrue[{#,#^2},PalindromeQ]&](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 20 2018 *)
is(n) = digits(n)==Vecrev(digits(n)) && digits(n^2)==Vecrev(digits(n^2)) \\ Felix Fröhlich, Jun 21 2017
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