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 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

%I

%S 13,157,913,4513,14647,19201,19291,19813,20191,27778,31828,34825,

%T 37471,39586,40297,50386,53536,53842,54913,62986,64021,70267,76513,

%U 78241,82597,89356,98347,100147,100597,103909,106528,111847,115024,117391,125986,128047

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

%C All terms are of form 9k+4. [_Zak Seidov_, Jun 04 2010]

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

%H Paolo P. Lava, <a href="/A072841/b072841.txt">Table of n, a(n) for n = 1..1000</a> (first 519 terms from Zak Seidov)

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

%t okQ[n_] := Module[{idn = IntegerDigits[n^2]}, Sort[idn] == Sort[IntegerDigits[(n + 1)^2]]]; Select[Range, okQ]

%o (PARI) isok(n) = vecsort(digits(n^2)) == vecsort(digits((n+1)^2)); \\ _Michel Marcus_, Sep 30 2016

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Aug 09 2002

%E Terms from 100147 onward from _N. J. A. Sloane_, May 24 2010

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)