A358984 - OEIS

%I #45 Jan 07 2023 04:32:49

%S 3,8,19,0,169,896,1496,3334,21789,79403,239439,651236,1670022,3015650,

%T 27292097,55608749,234846164,366081231,2594727780,6395506991

%N The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.

%C Number of terms of A061230 which are n digits long.

%H Nicolay Avilov, <a href="https://problems.ru/view_problem_details_new.php?id=76503">Problem of the Moscow Mathematical Olympiad, 1945</a> (in Russian).

%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%e a(1) = 3 because there are 3 single-digit numbers: 0, 2, 8 such that b + b = m^2, for example, 8 + 8 = 16 = 4^2;

%e a(2) = 8 because there are 8 two-digit numbers: 29, 38, 47, 56, 65, 74, 83, 92 such that bc + cb = m^2, for example, 29 + 92 = 121 = 11^2.

%t a[n_]:=Length[Select[Table[k, {k, 10^(n-1),10^n-1}],IntegerQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]]&]]; Array[a,10] (* _Stefano Spezia_, Dec 09 2022 *)

%o (Python)

%o from math import isqrt

%o def s(n): return isqrt(n)**2 == n

%o def c(n): return s(n + int(str(n)[::-1]))

%o def a(n): return 3 if n == 1 else sum(1 for k in range(10**(n-1), 10**n) if c(k))

%o print([a(n) for n in range(1, 7)]) # _Michael S. Branicky_, Dec 08 2022

%Y Cf. A056964, A061230, A356648.

%K nonn,base,more

%O 1,1

%A _Nicolay Avilov_, Dec 08 2022

%E a(9)-a(10) from _Michael S. Branicky_, Dec 08 2022

%E a(11)-a(20) from _Talmon Silver_, Dec 25 2022