A059846 a(n) is the least prime p, such that next_prime(2*p) - 2*p = 2*n - 1.

2, 7, 31, 71, 59, 331, 569, 263, 691, 977, 1091, 2089, 1487, 2417, 2797, 10223, 4987, 6427, 12743, 9811, 17041, 29423, 12739, 20323, 20147, 17839, 53017, 53693, 17033, 67261, 151169, 106357, 129517, 185153, 77969, 253609, 185477, 140717

Offset

1,1

Comments

Previous name was: Smallest p primes which give q=2p+2n-1 primes. Smallest Sophie Germain primes generalized in a possible way: 1 is replaced by 2n-1.

Links

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

Formula

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

a(n) = (A059847(n) - (2*n-1))/2. - Amiram Eldar, Feb 08 2025

Example

For n = 1, 2, 3, 4, ..., 2*n-1 = 1, 3, 5, 7, ... and 2*{2, 7, 31, 71, ...} + {1, 3, 5, 7, ...} = {5, 17, 67, 149, ...}.
For n = 75, a(75) = 140717 a prime gives 2*140717 + 75 = 281509, a new prime.

Mathematica

Array[(k = 1; While[NextPrime[2 #2] - 2 #2 != #1 & @@ {#, Prime[k]}, k++]; Prime[k]) &[2 # - 1] &, 38] (* Michael De Vlieger, Oct 12 2022 *)

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] = p); p = nextprime(p+1)); v; } \\ Amiram Eldar, Feb 08 2025

Crossrefs

Cf. A005384, A005385, A059847.

Sequence in context: A298169 A213721 A102162 * A343532 A034698 A115605

Adjacent sequences: A059843 A059844 A059845 * A059847 A059848 A059849

Keyword

nonn

Author

Labos Elemer, Feb 26 2001

Extensions

Offset corrected by Sean A. Irvine, Oct 12 2022

New name from Sean A. Irvine, Oct 12 2022

Status

approved