The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. Intersection of A005384 (Sophie Germain primes) and A072828. 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 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 Cf. A054723. Sequence in context: A074892 A074874 A051439 * A330951 A018116 A259643 Adjacent sequences:  A214870 A214871 A214872 * A214874 A214875 A214876 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Jul 30 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)