A116499
Numbers k such that the base-10 representation of k^2 has the structure dmmd, where d is a single digit and m is a string of digits.
Original entry on oeis.org
63565788, 777035126, 785900449264170834, 824735400720481514, 41969556121016094021, 7841042904081599033746826, 775474811976872476373043200886, 403578381989727694739321538082071713672671, 820657465670154825723396137907157085701046
Offset: 1
785900449264170834^2 = 6[17639516153625555][17639516153625555]6.
A116502
Squares with structure dmdmd, where d is a single digit and m a string of digits.
Original entry on oeis.org
69696, 56722567225, 95540955409, 1108033241108033241, 1220096161220096161, 4312080784312080784, 4432132964432132964, 4880384644880384644, 9024307889024307889, 9972299169972299169, 946308825294630882529, 11542927396115429273961, 46171709584461717095844
Offset: 1
309097^2 = a(3) = 9[5540]9[5540]9.
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w={}; Do[s = Reduce[(1 + 10^(1+e) + 100^(1+e)) d + 10 (1+10^(1+e)) x == y^2 && 0 <= x < 10^e && y>0, {x,y}, Integers]; If[s =!= False, w = Union[w, y^2 /. List@ ToRules@ s]], {e, 12}, {d, 9}]; w (* Giovanni Resta, Aug 01 2018 *)
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