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%I #3 Feb 11 2014 19:05:41
%S 6,55,116,161,255,511,666,969,996,5311,9666,9999,12255,12525,12552,
%T 41199,41919,41991,54246,54264,54426,71177,71717,71771,72255,72525,
%U 72552,77117,77171,77711,78055,83399,83939,83993,89999,97117,97171
%N Numbers n such that the "inventory" A063850 of n is a perfect square.
%H <a href="http://www.primepuzzles.net/puzzles/puzz_207.htm">The Inventory Sequences and Self-Inventoried Numbers</a> in www.primepuzzles.net (see Question 7)
%e The "inventory" of 511 is 1521 (one "5", two "1"s) = 39^2. Hence 1521 belongs to the sequence.
%t g[n_] := Module[{seen, r, d, l, i, t}, seen = {}; r = {}; d = IntegerDigits[n]; l = Length[d]; For[i = 1, i <= l, i++, t = d[[i]]; If[ ! MemberQ[seen, t], r = Join[r, IntegerDigits[Count[d, t]]]; r = Join[r, {t}]; seen = Append[seen, t]]]; FromDigits[r]]; Select[Range[10^5], IntegerQ[Sqrt[g[ # ]]] &]
%Y Cf. A063850.
%K base,nonn
%O 1,1
%A _Joseph L. Pe_, Jan 14 2003
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