A074395 A 7-way classification of the primes.

6, 1, 0, 5, 1, 4, 0, 5, 3, 0, 3, 4, 0, 5, 3, 2, 1, 2, 5, 1, 2, 5, 3, 4, 4, 0, 5, 1, 4, 2, 5, 3, 0, 3, 0, 3, 2, 5, 3, 2, 1, 2, 1, 4, 0, 5, 5, 5, 1, 4, 2, 1, 2, 3, 2, 3, 0, 3, 4, 0, 3, 2, 5, 1, 4, 2, 3, 2, 1, 4, 2, 5, 3, 2, 5, 3, 4, 4, 4, 2, 1, 2, 1, 2, 5, 3, 4, 4, 0, 5, 5, 5, 5, 5, 5, 3, 4, 0, 3, 2, 3, 2, 3, 0, 3

Offset

1,1

Comments

There are seven types of consecutive primes modulus 4 and whether or not they are twin primes. They are a (1, 3, paired), (3, 1, paired), (1, 3, not paired), (3, 1, not paired), (1, 1), (3, 3) and p(m)=2. Each case is mapped to a number from zero to six, respectively. Here the word paired means that the consecutive primes are twins.

The initial digit (6) occurs but once and the frequency for the digits 0 and 1 decreased with added terms.

Links

Table of n, a(n) for n=1..105.

Mathematica

a = {}; Do[p = Prime[n]; q = Prime[n + 1]; a = Append[a, Which[ Mod[p, 4] == 1 && Mod[q, 4] == 3 && p + 2 == q, 0, Mod[p, 4] == 3 && Mod[q, 4] == 1 && p + 2 == q, 1, Mod[p, 4] == 1 && Mod[q, 4] == 3 && p + 2 != q, 2, Mod[p, 4] == 3 && Mod[q, 4] == 1 && p + 2 != q, 3, Mod[p, 4] == 1 && Mod[q, 4] == 1, 4, Mod[p, 4] == 3 && Mod[q, 4] == 3, 5, p == 2, 6]]; p = q, {n, 1, 105}]; a

Crossrefs

Cf. A071696, A071698.

Sequence in context: A347237 A090203 A120113 * A355415 A262704 A335245

Adjacent sequences: A074392 A074393 A074394 * A074396 A074397 A074398

Keyword

nonn

Author

Roger L. Bagula, Sep 24 2002

Extensions

Edited and extended by Robert G. Wilson v, Oct 03 2002

Status

approved