|
|
A214873
|
|
Primes p such that 2*p + 1 is also prime and p + 1 is a highly composite number (definition 1).
|
|
2
|
|
|
3, 5, 11, 23, 179, 239, 359, 719, 5039, 55439, 665279, 6486479, 32432399, 698377679, 735134399, 1102701599, 20951330399, 3212537327999, 149602080797769599, 299204161595539199, 2718551763981393634806325317503999
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
An equivalent definition of this sequence: odd Sophie Germain primes that differ from a highly composite number by 1.
With the exception of 5, a subsequence of A002515 (Lucasian primes).
Except for first two terms, this is a subsequence of A054723.
Except for n = 2, 2*a(n) + 1 is a prime factor of A000225(a(n)) (i.e., 2*23 + 1 divides 2^23 - 1).
Conjecture: for n >= 5, GCD(A000032(a(n)), A000225(a(n))) = 2*a(n) + 1.
|
|
LINKS
|
|
|
EXAMPLE
|
23 is a term because both 23 and 47 are primes and also 24 is a highly composite number.
|
|
MATHEMATICA
|
lst = {}; a = 0; Do[b = DivisorSigma[0, n + 1]; If[b > a, a = b; If[PrimeQ[n] && PrimeQ[2*n + 1], AppendTo[lst, n]]], {n, 1, 10^6, 2}]; lst
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|