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

1,2

Comments

Sequence is a permutation of the positive integers.

Links

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

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

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 *)

Prog

(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, " "
}
(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

Crossrefs

Cf. A000463.

Sequence in context: A366260 A366946 A358534 * A350150 A111390 A349323

Adjacent sequences: A137439 A137440 A137441 * A137443 A137444 A137445

Keyword

easy,nonn

Author

Andy Martin, Apr 18 2008

Extensions

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

Status

approved