A309334 -id:A309334 - cp's OEIS frontend

A309333 The number of primes between two consecutive lucky primes, bounds excluded.

1, 1, 4, 0, 1, 4, 1, 0, 8, 4, 1, 5, 2, 0, 4, 7, 1, 3, 2, 2, 6, 1, 1, 5, 2, 6, 5, 3, 1, 1, 0, 1, 4, 6, 1, 4, 1, 4, 9, 5, 7, 0, 0, 2, 2, 5, 1, 3, 0, 8, 4, 1, 5, 2, 18, 0, 9, 3, 1, 1, 9, 2, 4, 5, 3, 2, 6, 5, 4, 9, 3, 4, 11, 1, 1, 3, 4, 20, 0, 8, 2, 4, 3, 3, 15, 6

Offset: 1

Hauke Löffler, Jul 24 2019

nonn

			a(1): Between the first two lucky primes (3, 7) there is one prime (5).
a(3): Between 13 and 31 there are 4 primes (17, 19, 23, 29).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000959, A031157, A309334, A176559.

def count_primes_between(a, b):
  return len(prime_range(a+1, b))
[count_primes_between(A031157[i], A031157[i+1]) for i in range (len(A031157[0:20])-1)]

A309381 Lucky primes k such that k+6 is also a lucky prime.

Original entry on oeis.org

7, 31, 37, 67, 73, 613, 991, 1087, 1117, 2467, 3301, 3307, 3607, 4561, 4987, 4993, 6367, 6373, 8263, 8641, 9643, 10903, 11827, 11953, 12373, 12547, 15187, 15901, 17047, 18043, 19603, 20353, 21751, 23671, 25147, 28837, 31033, 31231, 37957, 38707, 38917, 43201, 44383, 46021, 49627

Offset: 1

Robert Israel, Jul 26 2019

nonn

A031157(k) for k such that A309334(k)=6.

The minimum gap between lucky primes (after the first) is 6.

			37 and 37+6=43 are both lucky primes, so 37 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..1615

Cf. A031157, A309334.

N:= 10^5: # for terms <= N
L:= [seq(i,i=1..N+6,2)]:
for n from 2 while n < nops(L) do
  r:= L[n];
  L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);
od:
L:= convert(select(isprime,L),set):
A:= L intersect map(`-`,L,6):
sort(convert(A,list));

cp's OEIS Frontend

A309333 The number of primes between two consecutive lucky primes, bounds excluded.

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