|
|
A051024
|
|
Values of n for which pi_{4,3}(p_n) - pi_{4,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
|
|
14
|
|
|
2946, 50378, 50380, 50382, 50392, 50414, 50418, 50420, 50422, 50424, 50426, 50428, 50430, 50436, 50438, 50446, 50448, 50450, 50822, 50832, 50834, 50842, 50844, 50852, 50854, 50856, 50858, 50862, 50864, 50866, 50872, 50892, 50902
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This is a companion sequence to A051025.
Starting from a(27556) = 316064952540 the sequence includes the 8th sign-changing zone predicted by C. Bays et al. The sequence with the first 8 sign-changing zones contains 418933 terms (see a-file) with a(418933) = 330797040308 as its last term. - Sergei D. Shchebetov, Oct 06 2017
We also discovered the 9th sign-changing zone, which starts from 2083576475506, ends with 2083615410040, and has 13370 terms with pi_{4,3}(p) - pi_{4,1}(p) = -1. This zone is considerably lower than predicted by M. Deléglise et al. in 2004. - Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 30 2017
We also discovered the 10th sign-changing zone, which starts from 21576098946648, ends with 22056324317296, and has 481194 terms with pi_{4,3}(p) - pi_{4,1}(p) = -1. This zone is considerably lower than predicted by M. Deléglise et al. in 2004. - Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 28 2018
|
|
LINKS
|
M. Rubinstein, P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173-197.
|
|
MATHEMATICA
|
For[i=2; d=0, True, i++, d+=Mod[Prime[i], 4]-2; If[d==-1, Print[i]]]
(* Second program: *)
Position[Accumulate@ Array[Mod[Prime@ #, 4] - 2 &, 51000], -1][[All, 1]] (* Michael De Vlieger, Dec 30 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|