|
|
A166687
|
|
Numbers of the form x^2 + y^2 + 1, x, y integers.
|
|
4
|
|
|
1, 2, 3, 5, 6, 9, 10, 11, 14, 17, 18, 19, 21, 26, 27, 30, 33, 35, 37, 38, 41, 42, 46, 50, 51, 53, 54, 59, 62, 65, 66, 69, 73, 74, 75, 81, 82, 83, 86, 90, 91, 98, 99, 101, 102, 105, 107, 110, 114, 117, 118, 122, 123, 126, 129, 131, 137, 138, 145, 146, 147, 149, 150, 154, 158, 161
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A001481 is the main entry for this sequence.
As Ng points out (Lemma 2.2), each prime divides some member of this sequence: 2 divides a(2) = 2, 3 divides a(3) = 3, 5 divides a(4) = 5, 7 divides a(9) = 14, etc. - Charles R Greathouse IV, Jan 04 2016
|
|
LINKS
|
|
|
MAPLE
|
N:= 1000: # to get all terms <= N
S:= {seq(seq(x^2+y^2+1, y=0..floor(sqrt(N-1-x^2))), x=0..floor(sqrt(N-1)))}:
|
|
MATHEMATICA
|
Select[Range@ 162, Resolve[Exists[{x, y}, Reduce[# == x^2 + y^2 + 1, {x, y}, Integers]]] &] (* Michael De Vlieger, Jan 05 2016 *)
|
|
PROG
|
(PARI) is(n)=my(f=factor(n-1)); for(i=1, #f~, if(f[i, 1]%4==3 && f[i, 2]%2, return(0))); 1 \\ Charles R Greathouse IV, Jan 04 2016
(PARI) list(lim)=my(v=List(), t); lim\=1; for(m=0, sqrtint(lim-1), t=m^2+1; for(n=0, min(sqrtint(lim-t), m), listput(v, t+n^2))); Set(v) \\ Charles R Greathouse IV, Jan 05 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|