A229081 Numbers n such that there exists a square m^2 with 3n^2 - n <= m^2 <= 3n^2 + n.

1, 3, 4, 7, 8, 11, 12, 14, 15, 16, 18, 19, 22, 23, 26, 27, 29, 30, 33, 34, 37, 38, 40, 41, 42, 44, 45, 48, 49, 52, 53, 55, 56, 57, 59, 60, 63, 64, 67, 68, 70, 71, 74, 75, 78, 79, 82, 83, 85, 86, 89, 90, 93, 94, 96, 97, 98, 100, 101, 104, 105, 108, 109, 111, 112, 113, 115, 116, 119, 120, 123, 124, 126

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

There is a square between 3*4^2-4 and 3*4^2+4 (44<=49<=52) but not between 3*5^2-5=70 and 3*5^2+5=80, so 4 is in sequence but not 5.

Maple

filter:= n -> ceil(sqrt(3*n^2-n))<=floor(sqrt(3*n^2+n)):
select(filter, [$1..200]); # Robert Israel, Jan 05 2020

Prog

(PARI) for(n=1, 200, for(i=-n, n, f=0; if(issquare(3*n*n+i), f=1; break)); if(f, print1(n, ", ")))
(Magma) [n: n in [1..130] | exists{3*n^2+i: i in [-n..n] | IsSquare(3*n^2+i)}]; // Bruno Berselli, Sep 13 2013

Crossrefs

Cf. A006451, A072221.

Sequence in context: A213373 A363353 A332059 * A070874 A187582 A288553

Adjacent sequences: A229078 A229079 A229080 * A229082 A229083 A229084

Keyword

nonn

Author

Ralf Stephan, Sep 13 2013

Status

approved