

A074395


A 7way classification of the primes.


0



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
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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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



