

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.


6



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
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OFFSET

1,1


COMMENTS

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


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)


EXAMPLE

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


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 *)


PROG

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


CROSSREFS

Sequence in context: A130868 A154414 A164623 * A244206 A159499 A125470
Adjacent sequences: A072838 A072839 A072840 * A072842 A072843 A072844


KEYWORD

nonn,base


AUTHOR

Harvey P. Dale, Aug 09 2002


EXTENSIONS

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


STATUS

approved



