A072021
Smallest solution to gcd(x, reverse(x)) = 5^n.
Original entry on oeis.org
5, 5200, 521000, 5213750, 521875, 5218750, 52130234375, 5734841796875, 57869714843750, 526046650390625, 5265674365234375, 52187008544921875, 526515306396484375, 5213023309008789062500, 5213596736358642578125, 5260466086273193359375, 526041911745452880859375
Offset: 1
For n = 4, gcd(521875, 578125) = 3125 = 5^4.
For n = 8, a(8) = 5734841796875 = 5^9*2936239, reverse(a(8)) = 5786971484375 = 5^8*71*208657.
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a(n) = {my(k = 1); while (gcd(k, fromdigits(Vecrev(digits(k)))) != 5^n, k++); k;} \\ Michel Marcus, Jul 13 2018
A072018
Numbers k for which gcd(k, reverse(k)) = 243 = 3^5.
Original entry on oeis.org
4899999987, 4989999897, 4999889997, 4999997889, 5889998997, 5889999969, 5898989997, 5898998988, 5899899789, 5899979979, 5899987998, 5899989699, 5899996989, 5979999879, 5988899997, 5988998898, 5989889979, 5989897998
Offset: 1
k = 4899999987 = 3*3*3*3*3*157*128437 and reverse(k) = 78999999984 = 2*2*2*2*3*3*3*3*3*3*2031893, gcd = 243. Numerous but not all solutions are obtained by inserting strings of 9's between digits of A071016. Further such regular transformations exist.
A072017
Numbers k such that gcd(k, reverse(k)) = 81 = 3^4, where reverse(x) = A004086(x).
Original entry on oeis.org
2899999989, 2989999899, 2999889999, 3799999899, 3898989999, 3899799999, 3899999988, 3979989999, 3988899999, 3989999898, 3989999979, 3998999889, 3999889998, 3999898989, 3999899799, 3999979989, 3999988899, 4699998999
Offset: 1
k = 3*3*3*3*3*449*64157 and reverse(k) = 2*2*3*3*3*3*31*67*14827, GCD = 81.
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