A096482 - OEIS

%I #27 Feb 15 2025 09:22:24

%S 3,67,31,401,241,211,773,2221,1913,7649,3229,1669,2477,10009,5749,

%T 33647,9973,14107,60821,130729,16141,15683,113233,86629,95651,74959,

%U 35617,388403,214993,557093,248909,637003,296843,448451,186481,1145899,1283603,1845637,795349,542603

%N a(n) = prime(prime(A096480(n))).

%C a(n) = prime(p) where p is the smallest prime such that prime(p+1) - prime(p) = 2*n.

%C Both a(n) and a(n) + 2*n are primes while pi(a(n)) = A096481(n) and pi(pi(a(n))) = A096480(n).

%H Amiram Eldar, <a href="/A096482/b096482.txt">Table of n, a(n) for n = 1..214</a> (terms 1..100 from Andrew Howroyd)

%F a(n) = A006450(A096480(n)) = prime(A096481(n)).

%F a(n) + 2*n = prime(1 + prime(A096480(n))).

%e a(2) = 67 = prime(19) since prime(19+1) - prime(19) = 71 - 67 = 2*2 and 19 is the smallest prime with this property.

%t Prime[Prime[Min[Flatten[Position[Table[Prime[Prime[n]+1]- Prime[Prime[n]], {n, 1, 5000}], 2*j]]], {j, 1, 100}]]]

%o (PARI) a(n) = {my(p=2); while((prime(p+1)-prime(p))!=2*n, p=nextprime(p+1)); prime(p)} \\ _Klaus Brockhaus_, Jun 27 2004

%o (PARI) a(n) = {my(p=2,k=1); forprime(q=3, oo, if(q==p+2*n && isprime(k), return(p)); p=q; k++)} \\ _Andrew Howroyd_, Dec 16 2024

%Y Cf. A000040, A006450, A073124, A072677, A096477, A096478, A096479, A096480, A096481.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 23 2004

%E a(31)-a(36) from _Klaus Brockhaus_, Jun 27 2004

%E a(37) onwards from _Andrew Howroyd_, Dec 16 2024