

A309334


Lucky prime gaps: differences between consecutive lucky primes.


3



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
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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



