A137442 n^2 followed by smallest integer not yet listed.

1, 2, 4, 3, 9, 5, 16, 6, 25, 7, 36, 8, 49, 10, 64, 11, 81, 12, 100, 13, 121, 14, 144, 15, 169, 17, 196, 18, 225, 19, 256, 20, 289, 21, 324, 22, 361, 23, 400, 24, 441, 26, 484, 27, 529, 28, 576, 29, 625, 30, 676, 31, 729, 32, 784, 33, 841, 34, 900, 35, 961, 37, 1024, 38

Offset: 1

Author

Andy Martin, Apr 18 2008

Keywords

• easy
• nonn

Comments

Sequence is a permutation of the positive integers.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000463.

Programs

Mathematica

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 *)
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 *)

PARI

lista(nn) = {for (n=1, nn, print1(n^2, ", ", n+round(sqrt(n)), ", "););} \\ Michel Marcus, Nov 02 2014

PARI

a(n) = if (n % 2, ((n+1)/2)^2, (n/2)+round(sqrt(n/2))); \\ Michel Marcus, Nov 02 2014

Ruby

# correct to any term:
sk_ct = 2
skip = 4
at = 1
(1..(1.0/0)).each{ |i|
if (at+=1) == skip
at+=1
sk_ct +=1
skip = sk_ct * sk_ct
end
print i*i, " ", at, " "
}

Ruby

# Simpler Ruby code, correct until i is so large that floating point rounding causes errors. I estimate this will be before i reaches 10000000000000000
(1..(1.0/0)).each{ |i|
print i*i, " ", i + (Math.sqrt(i) + 0.5).to_i, " "
}

Formula

Formula, generating two terms for every m: m^2, m + round(sqrt(m)).

IFTE(n mod 2 ==1, ((n+1)/2)^2, (n/2)+round(sqrt(n/2),0)). - Gerald Hillier, Nov 15 2010

Extensions

More terms from Robert G. Wilson v, May 31 2009