10*a(n) are exactly the terms in A322835 that are not multiples of 100.
m is a term if and only if R(m) is a term.
The product of the first and last digits of a term is a multiple of 10, i.e., the first and last digits of a term are the digit 5 and an even nonzero digit.
The sequence has an infinite number of terms. For instance, 601x065 is a term where x is a string of k repeated digits 6 and k >= 0, i.e., 601065, 6016065, 60166065, etc. Similarly numbers of the form 560x106 are also terms.
To see this, let a = 601*10^(3+k) + 65 + 6000*(10^k1)/9. Then R(a) = 56*10^(4+k) + 106 + 6000*(10^k1)/9. The number 10*a*R(a) can be written as 30360100*(10^(k + 3)  1)^2/9 whose square root is 5510*(10^(k + 3)  1)/3.
From Chai Wah Wu, Feb 18 2019: (Start)
22994x77005 is a term where x is a string of k repeated digits 9 and k >= 0. Let a = 22994*10^(5+k) + 77005 + 100000*(10^k1). Then R(a) = 50077*10^(5+k) + 49922 + 100000*(10^k1). The number 10*a*R(a) can be written as 11515436100*(10^(k+5)  1)^2, whose square root is 107310*(10^(k+5)  1).
23804x76195 is a term where x is a string of k repeated digits 9 and k >= 0. Let a = 23804*10^(5+k) + 76195 + 100000*(10^k1). Then R(a) = 59167*10^(5+k) + 40832 + 100000*(10^k1). The number 10*a*R(a) can be written as 14084942400*(10^(k+5)  1)^2, whose square root is 118680*(10^(k+5)  1).
If w is a term with decimal representation a, then the number n corresponding to the string axa is also a term, where x is a string of k repeated digits 0 and k >= 0. The number n = w*10^(k+m)+w = w*(10^(k+m)+1) where m is the number of digits of w. Note that n is also not a multiple of 10. Then R(n) = R(w)*10^(k+m)+R(w) = R(w)(10^(k+m)+1). Then 10*n*R(n) = 10*w*R(w)(10^(k+m)+1)^2 which is a square since w is a term.
The same argument shows that numbers corresponding to axaxa, axaxaxa, ..., are also terms.
For example, since 544968 is a term, so are 544968544968, 5449680544968, 54496800544968, 5449680054496800544968, etc.
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