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URL: https://oeis.org/A079054

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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).
6
-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
Chris Caldwell, Prime Gaps.
Joseph L. Pe, Prime Gap Tug of War. [Dead link]
Carlos Rivera, Puzzle 271. Prime gap tug of war, The Prime Puzzles & Problems Connection.
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
KEYWORD
easy,sign
AUTHOR
Joseph L. Pe, Feb 02 2003
STATUS
approved