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%I #30 Nov 03 2014 03:28:22
%S 1,2,4,3,9,5,16,6,25,7,36,8,49,10,64,11,81,12,100,13,121,14,144,15,
%T 169,17,196,18,225,19,256,20,289,21,324,22,361,23,400,24,441,26,484,
%U 27,529,28,576,29,625,30,676,31,729,32,784,33,841,34,900,35,961,37,1024,38
%N n^2 followed by smallest integer not yet listed.
%C Sequence is a permutation of the positive integers.
%H Harvey P. Dale, <a href="/A137442/b137442.txt">Table of n, a(n) for n = 1..1000</a>
%F Formula, generating two terms for every m: m^2, m + round(sqrt(m)).
%F IFTE(n mod 2 ==1, ((n+1)/2)^2, (n/2)+round(sqrt(n/2),0)). - _Gerald Hillier_, Nov 15 2010
%t f[s_List] := Block[{k = 1}, While[ MemberQ[s, k], k++ ]; Flatten@ Append[s, {((2 + Length@s)/2)^2, k}]]; Nest[f, {1, 2}, 33] (* _Robert G. Wilson v_, May 31 2009 *)
%t Module[{nn=40,sq,int,len},sq=Range[nn]^2;int=Complement[Range[nn],sq];len=Min[Length[int],nn];Riffle[Take[sq,len],Take[int,len]]](* _Harvey P. Dale_, Nov 05 2013 *)
%o (Ruby)
%o # correct to any term:
%o sk_ct = 2
%o skip = 4
%o at = 1
%o (1..(1.0/0)).each{ |i|
%o if (at+=1) == skip
%o at+=1
%o sk_ct +=1
%o skip = sk_ct * sk_ct
%o end
%o print i*i, " ", at, " "
%o }
%o (Ruby)
%o # Simpler Ruby code, correct until i is so large that floating point rounding causes errors. I estimate this will be before i reaches 10000000000000000
%o (1..(1.0/0)).each{ |i|
%o print i*i, " ", i + (Math.sqrt(i) + 0.5).to_i, " "
%o }
%o (PARI) lista(nn) = {for (n=1, nn, print1(n^2, ", ", n+round(sqrt(n)), ", "););} \\ _Michel Marcus_, Nov 02 2014
%o (PARI) a(n) = if (n % 2, ((n+1)/2)^2, (n/2)+round(sqrt(n/2))); \\ _Michel Marcus_, Nov 02 2014
%Y Cf. A000463.
%K easy,nonn
%O 1,2
%A _Andy Martin_, Apr 18 2008
%E More terms from _Robert G. Wilson v_, May 31 2009
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