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A273361 Numbers n such that the decimal number concat(6,n) is a square. 8

%I

%S 4,25,76,241,400,561,724,889,1009,1504,2001,2500,3001,3504,4009,4516,

%T 5025,5536,6049,6564,7081,7600,8121,8644,9169,9696,11524,13089,14656,

%U 16225,17796,19369,20944,22521,24100,25681,27264,28849,30436

%N Numbers n such that the decimal number concat(6,n) is a square.

%C Elements are squares of integers in (sqrt(61), sqrt(70)) * sqrt(10)^k without the leading 6 elements for nonnegative k. - _David A. Corneth_, May 20 2016

%H Nathan Fox, <a href="/A273361/b273361.txt">Table of n, a(n) for n = 1..10000</a>

%e 76 is a member because 676 = 26^2 is a square.

%e 0 is not a member because 60 is not a square.

%p t1:=[];

%p for k from 1 to 50000 do

%p if issqr(k+6*10^length(k)) then t1:=[op(t1), k]; fi;

%p od;

%p t1;

%t Select[Range[31000],IntegerQ[Sqrt[FromDigits[Join[{6}, IntegerDigits[ #]]]]]&] (* _Harvey P. Dale_, Feb 09 2019 *)

%o (MAGMA) [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(6)))]; // _Marius A. Burtea_, Mar 21 2019

%Y Cf. A272671, A273357, A273358, A273359, A273360, 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 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)