login
A059846
a(n) is the least prime p, such that next_prime(2*p) - 2*p = 2*n - 1.
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.
FORMULA
Min{p|p and q=2p+2n-1 are primes}.
EXAMPLE
For n=1,2,3,4, 2n-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 *)
CROSSREFS
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