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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..25
Wikipedia, Sophie Germain prime
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
Arkadiusz Wesolowski, Jul 30 2012
STATUS
approved