A137264 Prime number gaps read modulo 3.

1, 2, 2, 1, 2, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 1, 0, 0, 0, 2, 0, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 0, 1, 0, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0

Offset

1,2

Comments

Conjecture: The only digit that is repeated in the sequence is 0 except for n=2 and n=3 where 2 repeats. So 1 may be followed by 2 or 0; 2 may be followed by 1 or 0; 0 may be followed by 0 or 1 or 2. this has been confirmed for the first million prime gaps.

The conjecture is true, because any three numbers whose differences are (1, 1) or (2, 2) will form a complete residue system modulo 3, and hence one of them will be a multiple of 3. - Karl W. Heuer, Mar 16 2016

See comments at A269364. - Antti Karttunen, Mar 17 2016

Links

Table of n, a(n) for n=1..102.

Terence Tao, Biases between consecutive primes, blog entry March 14, 2016

Mathematica

n=1000; (*The length of the list*) Mod[Differences[Table[Prime[i], {i, n}]], 3]

Prog

(Scheme) (define (A137264 n) (modulo (A001223 n) 3)) ;; Antti Karttunen, Mar 16 2016

Crossrefs

Cf. A001223.

Cf. also A269364, A270189, A270190, A270191, A270192.

Sequence in context: A352248 A301475 A138328 * A289014 A193238 A323826

Adjacent sequences: A137261 A137262 A137263 * A137265 A137266 A137267

Keyword

easy,nonn

Author

Noel H. Patson (n.patson(AT)cqu.edu.au), Mar 12 2008

Status

approved