A352955 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..25.

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

PROG

(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

CROSSREFS

Cf. A255562 (starting with 3,5).

Sequence in context: A302455 A303237 A066950 * A214495 A162011 A123248

Adjacent sequences: A352952 A352953 A352954 * A352956 A352957 A352958

KEYWORD

nonn

AUTHOR

Michel Marcus, Apr 11 2022

EXTENSIONS

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

STATUS

approved