A309367 The number of lucky numbers between two consecutive primes, bounds excluded.

0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 0, 0, 2, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 3, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 2, 0, 0, 0, 0, 1

Offset

1,15

Links

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

Example

a(1) = 0 because between the first two primes (2,3) there are no lucky numbers.
a(4) = 1 because between 7 and 1 there is one lucky number (9).
a(15) = 2 because between 47 and 53 there are two lucky numbers (49, 51).

Maple

# uses[A000959List]
A309367List := proc(mx) local L, j;
L := convert(A000959List(ithprime(mx)), set):
j := n -> {seq(k, k = [$ithprime(n)+1..ithprime(n+1)-1])}:
seq(nops(j(n) intersect L), n = 1..mx) end:
A309367List(87); # Peter Luschny, Mar 27 2020

Prog

(Sage) # uses[lucky from A000959]
def lucky_range(a, b):
    return [l for l in lucky(b) if a <= l < b]
P = prime_range(250)
[len(lucky_range(P[i]+1, P[i+1])) for i in range(len(P)-1)]

Crossrefs

Cf. A000040, A000959, A309365.

Sequence in context: A378150 A125005 A378149 * A347709 A122179 A335877

Adjacent sequences: A309364 A309365 A309366 * A309368 A309369 A309370

Keyword

nonn

Author

Hauke Löffler, Jul 25 2019

Status

approved