A309334 Lucky prime gaps: differences between consecutive lucky primes.

4, 6, 18, 6, 6, 24, 6, 6, 48, 24, 12, 30, 18, 12, 18, 42, 24, 24, 18, 18, 42, 12, 12, 30, 24, 54, 36, 24, 12, 6, 12, 12, 30, 54, 12, 30, 18, 36, 60, 54, 54, 6, 12, 12, 18, 48, 6, 24, 6, 78, 30, 18, 42, 12, 156, 12, 72, 24, 12, 18, 66, 30, 30, 54, 24, 30, 48, 54

Offset: 1

Author

Hauke Löffler, Jul 24 2019

Keywords

• nonn

Comments

Since (except for 3) all lucky primes == 1 (mod 6), a(n) >= 6 for n >= 2. - Robert Israel, Jul 26 2019

Examples

			a(1) = 4 because difference between the first (3) and second (7) lucky prime is 4.
a(2) = 6 because difference between 7 and 13 is 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031157, A001223, A309333.

Programs

Maple

N:= 10^4: # for lucky primes up to 2*N+1
L:= [seq(2*i+1, i=0..N)]:
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:
LP:= select(isprime,L):
LP[2..-1]-LP[1..-2]; # Robert Israel, Jul 26 2019

SageMath

[A031157[i+1]-A031157[i] for i in range(100)]

Formula

a(n) = A031157(n+1) - A031157(n).