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A273360 Numbers n such that the decimal number concat(5,n) is a square. 8

%I

%S 29,76,184,329,476,625,776,929,1076,1529,1984,2441,2900,3361,3824,

%T 4289,4756,5225,5696,6169,6644,7121,7600,8081,8564,9049,9536,11225,

%U 12656,14089,15524,16961,18400,19841,21284,22729,24176,25625,27076

%N Numbers n such that the decimal number concat(5,n) is a square.

%C Elements are squares of integers in (sqrt(51), sqrt(60)) * sqrt(10)^k without the leading 5 elements for nonnegative k. - _David A. Corneth_, May 20 2016

%H Nathan Fox, <a href="/A273360/b273360.txt">Table of n, a(n) for n = 1..10000</a>

%e 76 is a member because 576 = 24^2 is a square.

%e 0 is not a member because 50 is not a square.

%p t1:=[];

%p for k from 1 to 50000 do

%p if issqr(k+5*10^length(k)) then t1:=[op(t1), k]; fi;

%p od;

%p t1;

%t Select[Range[30000],IntegerQ[Sqrt[5*10^IntegerLength[#]+#]]&] (* _Harvey P. Dale_, Jan 01 2019 *)

%o (MAGMA) [n: n in [1..10000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(5)))]; // _Marius A. Burtea_, Mar 21 2019

%Y Cf. A272671, A273357, A273358, A273359, A273361, A273362, A273363, A273364.

%K nonn,base

%O 1,1

%A _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)