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
Examples
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.
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.
Programs
-
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.
Formula
a(n) = sqrt(A358880(n)). - Michel Marcus, Dec 25 2022
Extensions
a(38) and beyond from Hugo Pfoertner, Dec 12 2022
Comments