A072841 Numbers k such that the digits of k^2 are exactly the same (albeit in different order) as the digits of (k+1)^2.

13, 157, 913, 4513, 14647, 19201, 19291, 19813, 20191, 27778, 31828, 34825, 37471, 39586, 40297, 50386, 53536, 53842, 54913, 62986, 64021, 70267, 76513, 78241, 82597, 89356, 98347, 100147, 100597, 103909, 106528, 111847, 115024, 117391, 125986, 128047

Offset: 1

Author

Harvey P. Dale, Aug 09 2002

Keywords

• nonn
• base

Comments

All terms are of form 9k+4. - Zak Seidov, Jun 04 2010

All numbers of the form 5500*10^k - 87, k >= 1 are terms, i.e., 54 followed by k 9's followed by a 13: 54913, 549913, 5499913, etc. - Enrico Munini, Feb 21 2023

Examples

			913 is included because 913^2 = 833569, 914^2 = 835396 and both 833569 and 835396 contain exactly the same set of digits.
		

References

• Boris A. Kordemsky, The Moscow Puzzles, p. 165 (1972).

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000 (first 519 terms from Zak Seidov)

Programs

Mathematica

okQ[n_] := Module[{idn = IntegerDigits[n^2]}, Sort[idn] == Sort[ IntegerDigits[ (n + 1)^2]]]; Select[Range[100000], okQ]
SequencePosition[Table[FromDigits[Sort[IntegerDigits[n^2]]],{n,130000}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 09 2020 *)

PARI

isok(n) = vecsort(digits(n^2)) == vecsort(digits((n+1)^2)); \\ Michel Marcus, Sep 30 2016

Extensions

Terms from 100147 onward from N. J. A. Sloane, May 24 2010