A371981 Number of primes between two successive Sophie Germain primes, with Sophie Germain primes not themselves included in the count.

0, 0, 1, 3, 0, 2, 2, 6, 0, 5, 1, 7, 0, 1, 7, 0, 1, 5, 1, 9, 8, 1, 2, 7, 2, 10, 7, 2, 0, 3, 3, 3, 2, 4, 15, 5, 7, 0, 1, 2, 8, 14, 0, 7, 13, 4, 1, 3, 4, 0, 5, 3, 1, 17, 9, 9, 0, 2, 3, 5, 4, 1, 0, 7, 2, 14, 7, 2, 6, 0, 6, 7, 0, 18, 0, 6, 1, 7, 9, 3, 2, 0, 5, 28, 5, 3, 3, 2, 1, 5, 6, 7, 3, 15, 2

Offset

1,4

Comments

Number of primes between A005384(n) and A005384(n+1).

Links

Table of n, a(n) for n=1..95.

Formula

a(n) = A000720(A005384(n+1)) - A000720(A005384(n)) - 1. - Michael De Vlieger, Apr 19 2024

Example

a(4) = 3 because there are 3 primes between 11 and 23: 13, 17 and 19.

Mathematica

-1 + Subtract @@ Map[PrimePi, {Last[#], First[#]}] & /@ Partition[Select[Prime[Range[500]], PrimeQ[2 # + 1] &], 2, 1] (* Michael De Vlieger, Apr 19 2024 *)

Prog

(Python)
from sympy import isprime
l = []
s = 0
for i in range(3, 3800):
    if isprime(i):
        if isprime(2*i + 1):
            l.append(s)
            s = 0
        else:
            s += 1
print(l)
(PARI) lista(nn) = my(vp = select(p->isprime(2*p+1), primes(nn)), wp = apply(primepi, vp)); vector(#wp-1, k, wp[k+1]-wp[k]-1); \\ Michel Marcus, May 21 2024

Crossrefs

Cf. A000720, A005384.

Sequence in context: A300722 A087625 A300720 * A280238 A154574 A119493

Adjacent sequences: A371978 A371979 A371980 * A371982 A371983 A371984

Keyword

nonn

Author

Alexandre Herrera, Apr 15 2024

Status

approved