A356648 -id:A356648 - cp's OEIS frontend

A358880 Squares of the form k + reverse(k) for at least one k.

4, 16, 121, 484, 625, 1089, 10201, 14641, 19881, 40804, 49284, 69696, 91809, 94249, 203401, 698896, 1002001, 1234321, 1490841, 1517824, 4008004, 4276624, 4460544, 4937284, 5313025, 6325225, 6895876, 6948496, 7706176, 9018009, 15665764, 15776784, 16120225

Offset: 1

Jon E. Schoenfield, Dec 04 2022

			56 + reverse(56) = 56 + 65 = 121 = 11^2, so 121 is a term.

Cf. A000290, A067030, A356648.

from math import isqrt
def aupto(lim): return sorted(set(t for t in (k + int(str(k)[::-1]) for k in range(1, lim+1)) if t <= lim and isqrt(t)**2 == t))
print(aupto(10**7)) # Michael S. Branicky, Dec 25 2022

a(n) = A356648(n)^2. - Michel Marcus, Dec 25 2022

A358984 The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.

Original entry on oeis.org

3, 8, 19, 0, 169, 896, 1496, 3334, 21789, 79403, 239439, 651236, 1670022, 3015650, 27292097, 55608749, 234846164, 366081231, 2594727780, 6395506991

Offset: 1

Nicolay Avilov, Dec 08 2022

Number of terms of A061230 which are n digits long.

			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;
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.

Nicolay Avilov, Problem of the Moscow Mathematical Olympiad, 1945 (in Russian).
Index to sequences related to Olympiads.
Index entries for sequences related to Reverse and Add!

Cf. A056964, A061230, A356648.

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 *)

from math import isqrt
def s(n): return isqrt(n)**2 == n
def c(n): return s(n + int(str(n)[::-1]))
def a(n): return 3 if n == 1 else sum(1 for k in range(10**(n-1), 10**n) if c(k))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Dec 08 2022

a(9)-a(10) from Michael S. Branicky, Dec 08 2022

a(11)-a(20) from Talmon Silver, Dec 25 2022

cp's OEIS Frontend

A358880 Squares of the form k + reverse(k) for at least one k.

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A358984 The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.

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