A256398 Palindromes of the form i^2 + reverse(i)^2.

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

Author

Bui Quang Tuan, Mar 28 2015

Keywords

• nonn
• base
• changed

Comments

Is 864666666468 the only term in this sequence that has an even number of digits? - Jon E. Schoenfield, Mar 30 2015

The next terms with an even number of digits are 5807785995877085, 56359464311346495365, and 943614966934439669416349, which are obtained for i = 37939066, 3553782166, 529145826418 (and their reverses). - Giovanni Resta, Aug 22 2025

Examples

			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
		

Links

• Bui Quang Tuan, Table of n, a(n) for n = 1..458

Crossrefs

Cf. A002113 (palindromes), A056964 (n+rev(n)).

Cf. A256437.

Programs

Mathematica

Sort@ DeleteDuplicates@ Select[Table[n^2 + FromDigits[Reverse[IntegerDigits@ n]]^2, {n, 10000}], Reverse@ IntegerDigits@ # == IntegerDigits@ # &] (* Michael De Vlieger, Mar 28 2015 *)

PARI

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

Extensions

Data corrected by Derek Orr, Mar 29 2015