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

2,1

Comments

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

Links

Table of n, a(n) for n=2..100.

Example

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

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 *)

Crossrefs

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

Sequence in context: A359824 A087429 A093075 * A254634 A108336 A279733

Adjacent sequences: A104117 A104118 A104119 * A104121 A104122 A104123

Keyword

nonn,easy

Author

Joseph L. Pe, Mar 06 2005

Status

approved