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A265109 a(n) = largest k such that prime(n) + A002110(k) is prime.

%I A265109 #36 Jan 16 2025 17:17:18
%S A265109 0,1,2,3,3,4,6,7,8,6,5,9,8,8,14,9,16,17,14,14,16,21,11,19,14,24,25,15,
%T A265109 18,11,28,12,8,19,16,22,35,31,36,25,31,16,40,30,23,41,39,35,10,32,43,
%U A265109 38,24,41,19,35,23,55,54,24,53,50,57,62,48,36,64,21,45,54
%N A265109 a(n) = largest k such that prime(n) + A002110(k) is prime.
%C A265109 a(n) = n-1 iff a(n) is in A035346 for n > 1.
%H A265109 Michel Marcus, <a href="/A265109/b265109.txt">Table of n, a(n) for n = 1..1000</a>
%F A265109 a(n) < n.
%e A265109 a(4) = 3 because A002110(3) + prime(4) = A002110(3) + 7 = 37 is prime.
%o A265109 (PARI) a(n) = {my(k=1); while(k, if(ispseudoprime(prod(i=1, n-k, prime(i)) + prime(n)), return(n-k)); k++)}
%o A265109 (Python)
%o A265109 from itertools import count
%o A265109 from sympy import isprime, prime, primorial
%o A265109 def A002110(n): return primorial(n) if n > 0 else 1
%o A265109 def A265109(n):
%o A265109     pn = prime(n)
%o A265109     return next(k for k in range(n-1, -1, -1) if isprime(pn+A002110(k)))
%o A265109 print([A265109(n) for n in range(1, 31)]) # _Michael S. Branicky_, Jan 10 2025
%Y A265109 Cf. A000040, A002110, A035346, A100380.
%K A265109 nonn
%O A265109 1,3
%A A265109 _Altug Alkan_, Dec 01 2015