OFFSET
1,1
COMMENTS
I believe this is an infinite sequence, though a proof seems to be still far off. 155th term is 62910. There are probably infinitely many consecutive n^2+1 or (n^2+1)/2 primes. That is, n^2+1 and (n+2)^2+1 or (n^2+1)/2 and ((n+2)^2+1)/2 are both prime infinitely often.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
a(4)=10 (9^2+1)/2=41 and 10^2+1=101 and (11^2+1)/2=61 are prime.
MATHEMATICA
neoQ[n_]:=If[EvenQ[n], AllTrue[{((n-1)^2+1)/2, n^2+1, ((n+1)^2+1)/2}, PrimeQ], AllTrue[{(n-1)^2+1, (n^2+1)/2, (n+1)^2+1}, PrimeQ]]; Select[Range[ 6400], neoQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 19 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Garcia, Sep 23 2004
EXTENSIONS
More terms from Harvey P. Dale, Mar 19 2018
STATUS
approved