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A283560 Concatenation of the first n nonsquares (A000037).

%I A283560 #15 Feb 16 2025 08:33:42
%S A283560 2,23,235,2356,23567,235678,23567810,2356781011,235678101112,
%T A283560 23567810111213,2356781011121314,235678101112131415,
%U A283560 23567810111213141517,2356781011121314151718,235678101112131415171819,23567810111213141517181920
%N A283560 Concatenation of the first n nonsquares (A000037).
%C A283560 There are 5 primes in the first 6100 terms of this sequence, see A283561.
%H A283560 Robert Israel, <a href="/A283560/b283560.txt">Table of n, a(n) for n = 1..365</a>
%H A283560 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConsecutiveNumberSequences.html">Consecutive Number Sequences</a>
%p A283560 A[1]:= 2:
%p A283560 x:= 2:
%p A283560 for n from 2 to 20 do
%p A283560   if issqr(x+1) then x:= x+2 else x:= x+1 fi;
%p A283560   A[n]:= A[n-1]*10^(1+ilog10(x))+x;
%p A283560 od:
%p A283560 seq(A[n],n=1..20); # _Robert Israel_, Mar 13 2017
%t A283560 cns[n_]:=FromDigits[Flatten[IntegerDigits[Table[k+Floor[1/2+Sqrt[k]],{k,1,n}]]]]
%t A283560 Module[{nn=20,sqf},sqf=Select[Range[2,nn],!IntegerQ[Sqrt[#]]&];Table[FromDigits[Flatten[ IntegerDigits/@ Take[sqf,n]]],{n,Length[sqf]}]] (* _Harvey P. Dale_, Sep 07 2024 *)
%o A283560 (PARI) a(n)=my(s=""); for(k=1,n, s=Str(s, (sqrtint(4*k)+1)\2 + k)); eval(s) \\ _Charles R Greathouse IV_, Mar 10 2017
%Y A283560 Cf. A000037, A007908, A019521, A283561.
%K A283560 base,nonn
%O A283560 1,1
%A A283560 _XU Pingya_, Mar 10 2017