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Numbers which are not 1 larger than a nonzero square.
2

%I #9 Sep 06 2022 15:14:15

%S 1,3,4,6,7,8,9,11,12,13,14,15,16,18,19,20,21,22,23,24,25,27,28,29,30,

%T 31,32,33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,49,51,52,53,54,55,

%U 56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80

%N Numbers which are not 1 larger than a nonzero square.

%H Harvey P. Dale, <a href="/A164386/b164386.txt">Table of n, a(n) for n = 1..1000</a>

%F {1} U {A000027 \ A002522} (complement of A002522).

%F a(n) = n + floor(sqrt(n-1) + 1/2).

%e For n = 26, a(26) = n + [sqrt(n-1) + 1/2] = 26 + [sqrt(26-1) + 1/2] = 26 + [5.5] = 31.

%t With[{nn=100},Complement[Range[nn],Range[Floor[Sqrt[nn]]]^2+1]] (* _Harvey P. Dale_, Sep 06 2022 *)

%o (PARI) is(n)=!issquare(n-1) || n==1 \\ _Charles R Greathouse IV_, Sep 01 2015

%K nonn,easy

%O 1,2

%A _Jaroslav Krizek_, Aug 14 2009

%E Edited by _R. J. Mathar_, Aug 20 2009

%E Corrected by _Jaroslav Krizek_, Oct 24 2009