A358127 a(n) is the cardinality of the set of pairwise gcd's of {prime(1)+1, ..., prime(n)+1}.

1, 3, 4, 5, 5, 5, 5, 7, 8, 8, 8, 9, 9, 11, 12, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20, 21, 22, 22, 23, 23, 23, 23, 23, 24, 24, 26, 27, 29, 29, 30, 32, 32, 33, 35, 36, 36, 37, 37, 37, 37, 38, 38, 39, 39, 39, 39, 40, 40, 42, 42, 43, 43, 43, 44, 45, 45, 48, 48, 48, 48, 50, 50, 50, 50

Offset

2,2

Links

Table of n, a(n) for n=2..79.

Example

For n = 3 initial set is {2+1, 3+1, 5+1} and after applying gcd for each distinct pair of elements we get {1, 2, 3} set with cardinality of a(3) = 3.

Prog

(Python)
from sympy import nextprime
from math import gcd
from itertools import combinations
pr, terms = [2, 3], []
for i in range(100):
    terms.append(len(set([gcd(t[0]+1, t[1]+1) for t in combinations(pr, 2)])))
    pr.append(nextprime(pr[-1]))
print(terms)
(Python)
from math import gcd
from itertools import count, islice
from sympy import prime
def A358127_gen(): # generator of terms
    a, b = [3], set()
    for n in count(2):
        q = prime(n)+1
        b |= set(gcd(p, q) for p in a)
        yield len(b)
        a.append(q)
A358127_list = list(islice(A358127_gen(), 100)) # Chai Wah Wu, Nov 02 2022

Crossrefs

Cf. A008864, A356371, A214799.

Sequence in context: A220854 A122816 A064007 * A068568 A073169 A166268

Adjacent sequences: A358124 A358125 A358126 * A358128 A358129 A358130

Keyword

nonn

Author

Gleb Ivanov, Oct 30 2022

Status

approved