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A350100
Numbers k such that the prime gap between the consecutive primes p1 < k^2 < p2 sets a new record.
4
2, 3, 5, 11, 23, 30, 41, 50, 76, 100, 149, 159, 189, 345, 437, 509, 693, 1110, 1165, 5018, 14908, 18906, 19079, 28634, 38682, 80444, 105686, 185179, 265236, 269697, 409049, 558269, 1673629, 2965232, 3528015, 4292936, 34919969, 43957056, 148793437, 187220890, 424171123
OFFSET
1,1
COMMENTS
a(50) (in b-file) > 5*10^10, corresponding to A378904(50) > 613. - Hugo Pfoertner, Dec 23 2024
LINKS
EXAMPLE
n a(n) p1 a(n)^2 p2 gap=2*A378904(n)
1 2 3 4 5 2
2 3 7 9 11 4
3 5 23 25 29 6
4 11 113 121 127 14
5 23 523 529 541 18
6 30 887 900 907 20
7 41 1669 1681 1693 24
8 50 2477 2500 2503 26
MATHEMATICA
Module[{nn=4242*10^5, pg}, pg=Table[{n, NextPrime[n^2]-NextPrime[n^2, -1]}, {n, 2, nn}]; DeleteDuplicates[pg, GreaterEqual[#1[[2]], #2[[2]]]&]][[All, 1]] (* Harvey P. Dale, Jan 28 2023 *)
PROG
(PARI) a350100(limit) = {my(pmax=0); for(k=2, limit, my(kk=k*k, pp=precprime(kk), pn=nextprime(kk), d=pn-pp); if(d>pmax, print1(k, ", "); pmax=d))};
a350100(3000000)
(Python)
from itertools import count, islice
from sympy import prevprime, nextprime
def A350100_gen(): # generator of terms
c = 0
for k in count(2):
a = nextprime(m:=k**2)-prevprime(m)
if a>c:
yield k
c = a
A350100_list = list(islice(A350100_gen(), 20)) # Chai Wah Wu, Dec 17 2024
CROSSREFS
A378904 are the corresponding gaps, divided by 2.
Sequence in context: A118571 A118504 A215714 * A038905 A019405 A079848
KEYWORD
nonn,changed
AUTHOR
Hugo Pfoertner, Dec 25 2021
STATUS
approved