|
| |
|
|
A349519
|
|
a(n)=x is the least prime with pi(x,4,3) - pi(x,4,1) = 1-n where pi(x,4,k) is the number of primes 4*j + k <= x.
|
|
1
|
|
|
|
2, 26861, 616897, 616909, 616933, 623641, 623653, 623669, 623681, 12315529, 12315581, 12315613, 12315617, 12362653, 12362657, 12362717, 12362741, 12362981, 12362989, 12365033, 12365057, 12365153, 12365173, 12365201, 12366589, 951821281
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The difference d(x) = pi(x,4,3) - pi(x,4,1) changes sign infinitely often, see link "Prime Quadratic Effect". But this does not say anything about the amplitudes of these oscillations. For diagrams, see A349518, "Oscillations of d(x)". If d(x) has no lower limit, the current sequence is infinite. Regarding the upper limit, see A349518.
Note the gaps between 2, 26861 and 616897, 623681 and 12315529, 12366589 and 951821281.
|
|
|
LINKS
|
Table of n, a(n) for n=1..26.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.
|
|
|
EXAMPLE
|
primes 4*j+1: 5, 13, 17, ...
4*j+3: 3, 7, 11, ...
d(x) = pi(x,4,3) - pi(x,4,1)
.
n x pi(x,4,3) pi(x,4,1) d(x)=1-n?
- ----- --------- --------- -----------
1 2 0 0 0=0 true a(1) = 2
2 3 1 0 1=-1 false a(2) != 3
2 5 1 1 2=-1 false a(2) != 5
...........................
2 26861 1472 1473 -1=-1 true a(3) = 26861
|
|
|
PROG
|
(Maxima) block(w:[2], su:0, sum:0, n:1, p:2, nmax: 25,
/* returns nmax terms */
while n<nmax do(
p: next_prime(p), su:su+mod(p, 4)-2,
if su<sum then(n:n+1, sum:su, w: append(w, [p]) ) ) ,
w);
|
|
|
CROSSREFS
|
Cf. A038691, A007350.
Sequence in context: A237521 A131558 A133857 * A232869 A153912 A247790
Adjacent sequences: A349516 A349517 A349518 * A349520 A349521 A349522
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Gerhard Kirchner, Nov 20 2021
|
|
|
STATUS
|
approved
|
| |
|
|
