# [seqfan] prime congruences: A157010 and A042987

Richard Mathar mathar at strw.leidenuniv.nl
Sun Feb 22 21:18:51 CET 2009

```The author of A157010 claims that his sequence is different
from A042987, but does not give an argument. Using my two
hand's fingers, and looking at the congruences 0 (mod 8)
(empty set for primes) 1 mod 8, 2 mod 8 (contains only the 2)
3 mod 8, (4 mod 8 empty set for primes, divisor 4), 5 mod 8, (6 mod 8 empty
set for primes, divisor 2), 7 mod 8, I get prime classifications into the non-empty sets
1 mod 8
2 mod 8 (member p=2 only)
3 mod 8
5 mod 8
7 mod 8

So if the primes are not in  (1 mod 8), which is A157010,
they are clearly in (2 or 3 or 5 or 7) mod 8 which is A042987.
Am I overlooking some basics here?

http://research.att.com/~njas/sequences/?q=id:A157010|id:A042987
2,3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,101,103,107,109,127,131,139,149,151,157,163,167,173,179,181,191,197,199,211,223,227,229,239,251,263,269,271,277,283,293,307,311,317,331,347,349,359,367,373,379,
2,3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,101,103,107,109,127,131,139,149,151,157,163,167,173,179,181,191,197,199,211,223,227,229,239,251,263,269,271,277,

```