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.
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
Roger L. Bagula, Sep 24 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Oct 03 2002
STATUS
approved