OFFSET
1,1
COMMENTS
Twice A002383.
Also semiprimes n such that 2*n - 3 is a square. - Giovanni Teofilatto, Dec 29 2005. This coincidence was noticed by Andrew S. Plewe. Proof that this is the same sequence: If X is n^2+(n+1)^2+1, then 2X-3 is 4n^2+4n+1 = (2n+1)^2. And if 2X-3 is a square, then since it's odd, 2X-3 = (2n+1)^2 and X = n^2+(n+1)^2+1. - Don Reble, Apr 18 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
EXAMPLE
a(1)=6 because 1^2 + 2^2 + 1 = 6 = 2*3;
a(2)=14 because 2^2 + 3^2 + 1 = 14 = 2*7;
a(3)=26 because 3^2 + 4^2 + 1 = 26 = 13*2.
MATHEMATICA
2(#^2 + # + 1) & /@ Select[ Range[144], PrimeQ[ #^2 + # + 1] &] (* Robert G. Wilson v, May 28 2005 *)
fQ[n_] := Plus @@ Last /@ FactorInteger@n == 2 && IntegerQ@Sqrt[2n - 3]; Select[ Range@43513, fQ[ # ] &] (* Robert G. Wilson v *)
PROG
(PARI) for(n=2, 100000, if(bigomega(n)==2&&issquare(2*n-3), print1(n, ", "))) /* Lambert Herrgesell */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, May 21 2005
EXTENSIONS
Edited by Robert G. Wilson v, May 28 2005
Re-edited by N. J. A. Sloane, Apr 18 2007
STATUS
approved