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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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 -
Maple
filter:= n -> ceil(sqrt(3*n^2-n))<=floor(sqrt(3*n^2+n)): select(filter, [$1..200]); # Robert Israel, Jan 05 2020
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PARI
for(n=1,200,for(i=-n,n,f=0;if(issquare(3*n*n+i),f=1;break));if(f,print1(n,",")))