The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A074395 A 7-way 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 03:32 EST 2023. Contains 367468 sequences. (Running on oeis4.)