[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A356648
Numbers whose square is of the form k + reversal of digits of k, for some k.
3
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
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