A256398
Palindromes of the form i^2 + reverse(i)^2.
Original entry on oeis.org
0, 2, 8, 101, 242, 404, 585, 909, 10001, 12221, 14841, 20402, 24642, 40004, 44244, 48884, 50805, 90009, 96269, 1000001, 1030301, 1080801, 1210121, 1244421, 1298921, 1440441, 1478741, 1690961, 2004002, 2234322, 2468642, 2484842, 4000004, 4050504, 4410144
Offset: 1
Palindrome 585 is in the sequence because 585 = 12^2 + 21^2.
The smallest term that can be obtained in more than one way is 125484521 = 11020^2 + 2011^2 = 11200^2 + 211^2. Are there any terms that can be obtained in more than two ways? - _Jon E. Schoenfield_, Mar 30 2015
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Sort@ DeleteDuplicates@ Select[Table[n^2 + FromDigits[Reverse[IntegerDigits@ n]]^2, {n, 10000}], Reverse@ IntegerDigits@ # == IntegerDigits@ # &] (* Michael De Vlieger, Mar 28 2015 *)
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rev(n)=r="";d=digits(n);for(i=1,#d,r=concat(Str(d[i]),r));eval(r)
v=[];for(n=0,10^4,if(rev(P=(n^2+rev(n)^2))==P,v=concat(v,P)));vecsort(v,,8) \\ Derek Orr, Mar 29 2015
A256495
Palindromes i such that 2*i^2 is a palindrome.
Original entry on oeis.org
0, 1, 2, 11, 101, 111, 1001, 1111, 10001, 10101, 11011, 100001, 101101, 110011, 1000001, 1001001, 1010101, 1100011, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 1000000001, 1000110001, 1001001001, 1010000101
Offset: 1
Palindrome 11 is in the sequence because 2*11^2 = 242, a palindrome.
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dmax:= 11: # to get all terms with at most dmax digits
revdigs:= proc(n)
local L,i;
L:= convert(n,base,10);
add(10^(i-1)*L[-i],i=1..nops(L));
end proc:
filter:= proc(n) local L;
L:= convert(2*n^2,base,10);
L = ListTools:-Reverse(L)
end proc:
A:= {}:
for d from 1 to dmax do
if d::even then
A:= A union select(filter, {seq(10^(d/2)*x + revdigs(x), x=10^(d/2-1)..10^(d/2)-1)})
else
m:= (d-1)/2;
A:= A union select(filter, {seq(seq(10^(m+1)*x + y*10^m + revdigs(x), y=0..9),x=10^(m-1)..10^m-1)})
fi
od:
A; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(A,list)); # Robert Israel, Apr 13 2015
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palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[
Range@ 10000000, palQ@ # && palQ[#^2 + FromDigits[Reverse@ IntegerDigits@ #]^2] &] (* Michael De Vlieger, Mar 31 2015 *)
Select[Range[0,10101*10^5],AllTrue[{#,2#^2},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 26 2020 *)
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ispal(n) = my(d = digits(n)); Vecrev(d) == d;
lista(nn) = {for (n=0, nn, if (ispal(n) && ispal(2*n^2), print1(n, ", ")););} \\ Michel Marcus, Mar 31 2015
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