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
Robert Israel, Table of n, a(n) for n = 1..10000
Jia Hong Ray Ng, Quarternions and the four square theorem, 2008 Summer VIGRE Program for Undergraduates
Yu-Chen Sun and Hao Pan, The Green-Tao theorem for primes of the form x^2 + y^2 + 1, Monatshefte für Mathematik vol. 189 (2019), pp. 715-733. arXiv:1708.08629 [math.NT]
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)))}:
sort(convert(S, list)); # Robert Israel, Jan 05 2016
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
N. J. A. Sloane, Mar 05 2010
STATUS
approved