A175897 Numbers n with property that n*prime(n)+(n+1)*prime(n+1) is a perfect square s^2.

1681, 3146, 5917, 308950, 10553441, 10553550, 4273262954, 9781980985

Offset: 1

Author

Zak Seidov, Oct 11 2010

Keywords

• more
• nonn

Comments

Or, numbers n with property that A033286(n)+A033286(n+1) is a perfect square s^2, A033286(n)=n*(n-th prime). [From Zak Seidov, Oct 12 2010]

a(9) > pi(4*10^12). [From Donovan Johnson, Oct 22 2010]

Examples

			{n,s}: {1681,6943},{3146,13487},{5917,26299},{308950,1647737}, {10553441,63320647},{10553550,63321299}; no more n's up to 2*10^8.
		

Programs

Mathematica

Position[Total/@Partition[Table[n Prime[n],{n,310000}],2,1],? (IntegerQ[ Sqrt[#]]&)]//Flatten (* The program generates the first four terms of the sequence. To generate more, Increase the Range constant, but the program may take a long time to run. *) (* _Harvey P. Dale, Feb 05 2022 *)

PARI

isok(n) = issquare(n*prime(n)+(n+1)*prime(n+1)); \\ Michel Marcus, Oct 19 2013

Extensions

a(7)-a(8) from Donovan Johnson, Oct 22 2010