A079465 Numbers k such that the "inventory" A063850 of k is a perfect square.

6, 55, 116, 161, 255, 511, 666, 969, 996, 5311, 9666, 9999, 12255, 12525, 12552, 41199, 41919, 41991, 54246, 54264, 54426, 71177, 71717, 71771, 72255, 72525, 72552, 77117, 77171, 77711, 78055, 83399, 83939, 83993, 89999, 97117, 97171

Offset: 1

Author

Joseph L. Pe, Jan 14 2003

Keywords

• base
• nonn

Examples

			The "inventory" of 511 is 1521 (one "5", two "1"s) = 39^2. Hence 1521 belongs to the sequence.
		

Links

• Carlos Rivera, Puzzle 207. The Inventory Sequences and Self-Inventoried Numbers, The Prime Puzzles & Problems Connection. See Question 7.

Crossrefs

Cf. A063850.

Programs

Mathematica

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[ # ]]] &]