A356648 Numbers whose square is of the form k + reversal of digits of k, for some k.

2, 4, 11, 22, 25, 33, 101, 121, 141, 202, 222, 264, 303, 307, 451, 836, 1001, 1111, 1221, 1232, 2002, 2068, 2112, 2222, 2305, 2515, 2626, 2636, 2776, 3003, 3958, 3972, 4015, 4081, 7975, 8184, 9757, 10001, 10201, 10401, 11011, 11121, 11211, 12012, 12021, 12221, 13046, 16581, 20002

Offset

1,1

Comments

Square roots of the squares in A067030.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..2253, using results from participants Sebastian and l4m2 at the Code Golf challenge.

Nicolay Avilov, Problem 2422. Mirror numbers (in Russian).

Code Golf Stack Exchange, RADD decomposition of an integer, coding challenge started Jan 01 2023.

Formula

a(n) = sqrt(A358880(n)). - Michel Marcus, Dec 25 2022

Example

4 is a term since 4^2 = 16 = 8 + 8;
11 is a term since 11^2 = 121 = 29 + 92 is sum of k=29 and its reversal 92;
22 is a term since 22^2 = 484 = 143 + 341;
10201 is a term since 10201^2 = 104060401 = 100030400 + 4030001.

Prog

(PARI) L=vectorsmall(100000);
\\ Takes a few minutes of CPU time
for (k=1, 2*10^8, my(d=digits(k), r=fromdigits(Vecrev(d)), s); if (issquare(k+r, &s), L[s]=1));
for (k=1, 21000, if(L[k], print1(k, ", "))) \\ Hugo Pfoertner, Dec 13 2022
(C++, Haskell) See Code Golf link.

Crossrefs

Cf. A056964, A061230, A067030, A358880, A358984.

Sequence in context: A295947 A018774 A102608 * A290439 A018259 A018480

Adjacent sequences: A356645 A356646 A356647 * A356649 A356650 A356651

Keyword

nonn,base

Author

Nicolay Avilov, data a(10)-a(37) from Oleg Sorokin, Dec 10 2022

Extensions

a(38) and beyond from Hugo Pfoertner, Dec 12 2022

Status

approved