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A069919
Squares which repeat with at least two full periods when written in base 10.
10
69696, 56722567225, 95540955409, 1108033241108033241, 1220096161220096161, 4312080784312080784, 4432132964432132964, 4880384644880384644, 9024307889024307889, 9972299169972299169, 225607697225607697225, 946308825294630882529, 1322314049613223140496
OFFSET
1,1
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..21 (terms < 10^24)
EXAMPLE
264^2 = 69|69|6 in base 10.
15020242915^2 = 225607697|225607697|225 in base 10.
36363636364^2 = 13223140496|13223140496 in base 10.
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 *)
CROSSREFS
Cf. A071128 (base 2) - A071135 (base 9), A116502.
Sequence in context: A224324 A053075 A154818 * A116502 A190934 A043600
KEYWORD
base,nonn
AUTHOR
Erich Friedman, Apr 25 2002
EXTENSIONS
Corrected and extended by Jason Earls, Jun 16 2002
Data corrected and extended by Giovanni Resta, Aug 01 2018
STATUS
approved