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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.

%I A352955 #12 Jan 05 2025 19:51:42
%S A352955 11,19,3,73,5,1163,17,2309,3,147773,7,2364361,43,75659509,109,
%T A352955 605275963,601,732718084457515921,2767,1500606636968992603441,145687,
%U A352955 192077649532031053094761,10273,103120902879077884687304760481759,5036623
%N 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.
%C A352955 a(26) > 4.34448*10^41. - _Michael S. Branicky_, Apr 12 2022
%H A352955 Jeremy F. Alm and Taylor Herald, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/54-1/AlmHerald09152015.pdf">A Note on Prime Fibonacci Sequences</a>, Fibonacci Quart. 54 (2016), no. 1, 55-58.
%o A352955 (Python)
%o A352955 from sympy import isprime, factorint
%o A352955 from itertools import islice
%o A352955 def rem2(n):
%o A352955     while n%2 == 0: n //= 2
%o A352955     return n
%o A352955 def agen():
%o A352955     b, c = 11, 19
%o A352955     yield 11
%o A352955     while True:
%o A352955         yield c
%o A352955         k = (c+2)//b + 1
%o A352955         m = b*k
%o A352955         while not isprime(m-c) or min(factorint(rem2(k)), default=b+1) < b:
%o A352955             m += b
%o A352955             k += 1
%o A352955         b, c = c, m-c
%o A352955 print(list(islice(agen(), 17))) # _Michael S. Branicky_, Apr 12 2022
%Y A352955 Cf. A255562 (starting with 3,5).
%K A352955 nonn
%O A352955 1,1
%A A352955 _Michel Marcus_, Apr 11 2022
%E A352955 a(18)-a(25) from _Michael S. Branicky_, Apr 11 2022