A059847 a(n) = 2*p + 2*n - 1, where p is the least prime such that next_prime(2*p) - 2*p = 2*n - 1.

5, 17, 67, 149, 127, 673, 1151, 541, 1399, 1973, 2203, 4201, 2999, 4861, 5623, 20477, 10007, 12889, 25523, 19661, 34123, 58889, 25523, 40693, 40343, 35729, 106087, 107441, 34123, 134581, 302399, 212777, 259099, 370373, 156007, 507289, 371027

Offset

1,1

Comments

Previous name was: a(n)=2*p+2n-1, the smallest prime q such that p=[q-(2n-1)]/2 is prime. A special generalization of safe primes: 1 is replaced with 2n-1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..201

Formula

Min{p|p and q=(p-2n+1)/2, p and q are primes}.

a(n) = 2*A059846(n) + 2*n - 1. - Amiram Eldar, Feb 08 2025

Example

For n = 8, 2*n-1 = 15, a(8) = 541 because (541-15)/2 = 263 is the corresponding generalized Sophie Germain prime and {541, 263} is the smallest pair belonging to 15.

Mathematica

a[n_] := Module[{p = 2, m = 2*n-1}, While[NextPrime[2*p] != 2*p + m, p = NextPrime[p]]; 2*p + m]; Array[a, 37] (* Amiram Eldar, Feb 08 2025 *)

Prog

(PARI) list(len) = {my(v = vector(len), c = 0, i, p = 2); while(c < len, i = (nextprime(2*p+1) - 2*p + 1)/2; if(i <= len && v[i] == 0, c++; v[i] = 2*p + 2*i - 1); p = nextprime(p+1)); v; } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A005384, A005385, A059846.

Sequence in context: A012765 A062613 A153323 * A149678 A149679 A149680

Adjacent sequences: A059844 A059845 A059846 * A059848 A059849 A059850

Keyword

nonn

Author

Labos Elemer, Feb 26 2001

Extensions

New name from Amiram Eldar, Feb 08 2025

Status

approved