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A367805 a(1) = 0; for n > 1, a(n) is the least positive integer k for which k*prime(n) + 2 is prime.

%I A367805 #49 Jan 04 2024 21:10:41
%S A367805 0,1,1,3,1,3,1,3,3,1,5,3,1,3,7,7,1,5,5,1,5,3,3,3,3,1,3,1,5,9,3,7,1,3,
%T A367805 1,5,5,3,3,3,1,5,1,5,1,3,9,5,1,9,3,1,15,7,3,15,1,9,11,1,9,3,21,1,3,3,
%U A367805 5,3,1,3,3,15,3,5,9,3,13,3,19,3,1,15,1,3,3,9,13,3,1,15
%N A367805 a(1) = 0; for n > 1, a(n) is the least positive integer k for which k*prime(n) + 2 is prime.
%H A367805 Alois P. Heinz, <a href="/A367805/b367805.txt">Table of n, a(n) for n = 1..10000</a>
%F A367805 a(n) = (A279756(n) - 2)/A000040(n).
%F A367805 a(n) = 1 <=> n in A029707.
%e A367805 For n = 4: a(4) = 3, because prime(4) = 7, 3*7 + 2 = 23 which is prime.
%p A367805 a:= proc(n) local p, q, r; p:= ithprime(n); q:= p;
%p A367805       while irem(q-2, p, 'r')<>0 do q:= nextprime(q) od; r
%p A367805     end:
%p A367805 seq(a(n), n=1..99);  # _Alois P. Heinz_, Dec 04 2023
%t A367805 nmax=90; a[1]=0; For[n=2, n<=nmax, n++, For[k=1, k>0, k++, If[PrimeQ[k*Prime[n]+2], a[n]=k; k=-1]]]; Array[a,nmax] (* _Stefano Spezia_, Dec 04 2023 *)
%o A367805 (PARI) a(n) = if (n==1, 0, my(k=1, p=prime(n)); while (!isprime(k*p+2), k++); k); \\ _Michel Marcus_, Dec 02 2023
%o A367805 (Python)
%o A367805 from itertools import count, dropwhile
%o A367805 from sympy import prime, isprime
%o A367805 def A367805(n):
%o A367805     if n==1:
%o A367805         return 0
%o A367805     else:
%o A367805         p = prime(n)
%o A367805         return next(dropwhile(lambda x:not isprime(x*p+2),count(1))) # _Chai Wah Wu_, Jan 04 2024
%Y A367805 Cf. A000040, A029707, A035096, A117673, A279756, A001359.
%K A367805 nonn
%O A367805 1,4
%A A367805 _Frank Hollstein_, Dec 01 2023
%E A367805 More terms from _Michel Marcus_, Dec 02 2023