A161847 Denominator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).

2, 3, 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Author

Daniel Tisdale, Jun 20 2009

Keywords

• nonn
• frac

Comments

Conjecture: the sequence (prime((n+1)^2) - prime(n^2))/prime(n) converges to 4.

Examples

			The first few fractions are 5/2, 16/3, 6/1, 44/7, 54/11, ... = A161846/A161847.
		

Crossrefs

Cf. A000040, A011757, A161846 (numerators).

Programs

PARI

a(n) = denominator((prime((n+1)^2) - prime(n^2))/prime(n)); \\ Michel Marcus, May 14 2020

Formula

a(n) = denominator((A011757(n+1) - A011757(n))/A000040(n)). - Petros Hadjicostas, May 13 2020

Extensions

Keyword:frac added by R. J. Mathar, Jun 30 2009

Extended by Ray Chandler, May 06 2010

Various sections edited by Petros Hadjicostas, May 13 2020