A164515 Positive numbers not of the form n^2+2.

1, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80

Offset

1,2

Comments

Complement of A059100, and essentially also of A010000.

From Klaus Purath, Jan 22 2026: (Start)

This sequence is closed under multiplication.

The indices of the squares > 1 of this sequence are equal to the oblong numbers (A002378) such that a(k*(k+1)) = (k+1)^2. (End)

Links

Table of n, a(n) for n=1..71.

Formula

A000027 \ A059100.

a(n) = n + 1 + floor(sqrt(n-1) + 1/2), for n >= 2.

Mathematica

With[{upto=80}, Complement[Range[upto], Range[0, Floor[Sqrt[upto-2]]]^2+2]] (* Harvey P. Dale, Jun 22 2013 *)

Crossrefs

Sequence in context: A257542 A182757 A381255 * A298871 A298874 A266267

Adjacent sequences: A164512 A164513 A164514 * A164516 A164517 A164518

Keyword

nonn,easy

Author

Jaroslav Krizek, Aug 14 2009

Extensions

Redefined for simplicity by removing 2, R. J. Mathar, Aug 31 2009

Status

approved