A352955 a(n+2) is the smallest odd prime such that a(n) is the smallest odd prime divisor of a(n+1)+a(n+2), starting with a(1) = 11 and a(2) = 19.

11, 19, 3, 73, 5, 1163, 17, 2309, 3, 147773, 7, 2364361, 43, 75659509, 109, 605275963, 601, 732718084457515921, 2767, 1500606636968992603441, 145687, 192077649532031053094761, 10273, 103120902879077884687304760481759, 5036623

Offset: 1

Author

Michel Marcus, Apr 11 2022

Keywords

• nonn

Comments

a(26) > 4.34448*10^41. - Michael S. Branicky, Apr 12 2022

Links

• Jeremy F. Alm and Taylor Herald, A Note on Prime Fibonacci Sequences, Fibonacci Quart. 54 (2016), no. 1, 55-58.

Crossrefs

Cf. A255562 (starting with 3,5).

Programs

Python

from sympy import isprime, factorint
from itertools import islice
def rem2(n):
    while n%2 == 0: n //= 2
    return n
def agen():
    b, c = 11, 19
    yield 11
    while True:
        yield c
        k = (c+2)//b + 1
        m = b*k
        while not isprime(m-c) or min(factorint(rem2(k)), default=b+1) < b:
            m += b
            k += 1
        b, c = c, m-c
print(list(islice(agen(), 17))) # Michael S. Branicky, Apr 12 2022

Extensions

a(18)-a(25) from Michael S. Branicky, Apr 11 2022