A079054 a(n) = -1 if the closest prime to prime(n) is prime(n-1); = 1 if the closest prime to prime(n) is prime(n+1); = 0 if prime(n-1) and prime(n+1) are equally close to prime(n).

-1, 0, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 0, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 0, 1, -1, 0, 1, -1, 1, -1, 1, -1, 0, 1, 1, -1, -1, 1, -1, 1, 0, 0, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 0, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1

Offset

2

Comments

There is no gap before 2, so we start with prime 3.

Links

N. J. A. Sloane, Table of n, a(n) for n = 2..20000

Chris Caldwell, Prime Gaps [Broken link?]

Pe, J. L. Prime Gap Tug of War

C. Rivera, Puzzle 271: Prime gap tug of war.

Formula

a(n) = min(1, max(-1, A001223(n-1) - A001223(n))). - Charles R Greathouse IV, Nov 16 2012

Example

prime(1) = 2 is closer to prime(2) = 3 than prime(3) = 5, so a(2) = -1.

Maple

# From N. J. A. Sloane, Mar 13 2016
a:=[]; M:=120; for n from 2 to M-1 do
q:=ithprime(n); p:=prevprime(q); r:=nextprime(q);
if q-p < r-q then a:=[op(a), -1];
elif q-p=r-q then a:=[op(a), 0]; else a:=[op(a), 1]; fi;
od:
a;

Mathematica

Table[-Sign[Prime[n-1] - 2*Prime[n] + Prime[n+1]], {n, 2, 100}]

Prog

(PARI) p=2; q=3; forprime(r=5, 97, print1(sign(2*q-r-p)", "); p=q; q=r) \\ Charles R Greathouse IV, Nov 16 2012

Crossrefs

Cf. A092243 (cumulative sum, negated), A268343.

Sequence in context: A176412 A013596 A182394 * A131695 A324113 A105812

Adjacent sequences: A079051 A079052 A079053 * A079055 A079056 A079057

Keyword

easy,sign

Author

Joseph L. Pe, Feb 02 2003

Status

approved