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%I #38 May 14 2023 04:13:45
%S 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,
%T 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,
%U 0,0,1,1,0,0,0,1,2,1,0,1,0,2,0,0,0,0,1
%N The number of lucky numbers between two consecutive primes, bounds excluded.
%H Amiram Eldar, <a href="/A309367/b309367.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 0 because between the first two primes (2,3) there are no lucky numbers.
%e a(4) = 1 because between 7 and 1 there is one lucky number (9).
%e a(15) = 2 because between 47 and 53 there are two lucky numbers (49, 51).
%p # uses[A000959List]
%p A309367List := proc(mx) local L, j;
%p L := convert(A000959List(ithprime(mx)), set):
%p j := n -> {seq(k, k = [$ithprime(n)+1..ithprime(n+1)-1])}:
%p seq(nops(j(n) intersect L), n = 1..mx) end:
%p A309367List(87); # _Peter Luschny_, Mar 27 2020
%o (Sage) # uses[lucky from A000959]
%o def lucky_range(a, b):
%o return [l for l in lucky(b) if a <= l < b]
%o P = prime_range(250)
%o [len(lucky_range(P[i]+1, P[i+1])) for i in range(len(P)-1)]
%Y Cf. A000040, A000959, A309365.
%K nonn
%O 1,15
%A _Hauke Löffler_, Jul 25 2019
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