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A325152 Numbers whose squares can be expressed as the product of a number and its reversal. 0

%I #29 Aug 06 2019 10:09:45

%S 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,

%T 90,99,100,101,110,111,121,131,141,151,161,171,181,191,200,202,212,

%U 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

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

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

%C 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.

%C 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.

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

%e One way: 20^2 = 400 = 200 * 2.

%e Two ways: 2772^2 = 7683984 = 2772 * 2772 = 1584 * 4851.

%e Three ways: 2520^2 = 14400 * 441 = 25200 * 252 = 44100 * 144.

%e 403 is a member since 403^2 = 162409 = 169*961 (note that 403 is not a member of A281625).

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

%Y Cf. also A061917, A325151.

%Y Similar to but different from A281625.

%K nonn,base

%O 1,3

%A _Bernard Schott_, Apr 11 2019

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)