A325152 Numbers whose squares can be expressed as the product of a number and its reversal.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 110, 111, 121, 131, 141, 151, 161, 171, 181, 191, 200, 202, 212, 220, 222, 232, 242, 252, 262, 272, 282, 292, 300, 303, 313, 323, 330, 333, 343, 353, 363, 373, 383, 393, 400, 403, 404, 414, 424, 434

Offset

1,3

Comments

The corresponding squares are in A325148 and the numbers k such that k * rev(k) is a square are in A306273.

The squares of the first 47 terms of this sequence (from 0 to 242) can be expressed as the product of a number and its reversal in only one way; then a(48) = 252 and 252^2 = 252 * 252 = 144 * 441.

The first 65 terms of this sequence (from 0 to 400) are exactly the first 65 terms of A061917; then a(66) = 403, non-palindrome, is the first term of the sequence A325151.

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = sqrt(A325148(n)).

Example

One way: 20^2 = 400 = 200 * 2.
Two ways: 2772^2 = 7683984 = 2772 * 2772 = 1584 * 4851.
Three ways: 2520^2 = 14400 * 441 = 25200 * 252 = 44100 * 144.
403 is a member since 403^2 = 162409 = 169*961 (note that 403 is not a member of A281625).

Crossrefs

Cf. A325148, A325149, A083408, A325150, A307019.

Cf. also A061917, A325151.

Similar to but different from A281625.

Sequence in context: A084050 A281625 A169824 * A061917 A125289 A180482

Adjacent sequences: A325149 A325150 A325151 * A325153 A325154 A325155

Keyword

nonn,base

Author

Bernard Schott, Apr 11 2019

Status

approved