A104120 a(n) = (prime(n + 1) - prime(n))/2 (mod 2).

1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1

Offset: 2

Author

Joseph L. Pe, Mar 06 2005

Keywords

• nonn
• easy

Comments

Questions: Is s(n) = (1/n)*Sum_{i=2..n+1} a(i) > 1/2 for all n? Does s(n) --> 1/2?

Examples

			a(1) = (prime(2 + 1) - prime(2))/2 (mod 2) = (5 - 3)/2 (mod 2) = 1 mod 2 = 1.
		

Crossrefs

Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556-A330561.

Programs

Mathematica

Table[Mod[(Prime[i + 1] - Prime[i])/2, 2], {i, 2, 100}]
Mod[(#[[2]]-#[[1]])/2,2]&/@Partition[Prime[Range[2,110]],2,1] (* Harvey P. Dale, Oct 01 2018 *)