A069919 Squares which repeat with at least two full periods when written in base 10.
69696, 56722567225, 95540955409, 1108033241108033241, 1220096161220096161, 4312080784312080784, 4432132964432132964, 4880384644880384644, 9024307889024307889, 9972299169972299169, 225607697225607697225, 946308825294630882529, 1322314049613223140496
Offset: 1
Examples
264^2 = 69|69|6 in base 10. 15020242915^2 = 225607697|225607697|225 in base 10. 36363636364^2 = 13223140496|13223140496 in base 10.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..21 (terms < 10^24)
Programs
-
Mathematica
psq[b_, nd_] := Block[{sq={}, r, x}, Do[r = Mod[nd, p]; Do[x = (b^( Floor[nd/p] p) - 1)/(b^p - 1) t b^r + Floor[t/b^(p - r)]; If[ IntegerQ@ Sqrt@ x, AppendTo[ sq, x]], {t, b^(p - 1), b^p - 1}], {p, nd/2}]; sq]; Union @@ (psq[10, #] & /@ Range[11]) (* Giovanni Resta, Aug 01 2018 *)
Extensions
Corrected and extended by Jason Earls, Jun 16 2002
Data corrected and extended by Giovanni Resta, Aug 01 2018