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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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

Prog

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

Crossrefs

Cf. A031157, A001223, A309333.

Sequence in context: A061361 A332986 A113610 * A263319 A062046 A102020

Adjacent sequences: A309331 A309332 A309333 * A309335 A309336 A309337

Keyword

nonn

Author

Hauke Löffler, Jul 24 2019

Status

approved