|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|