OFFSET
1,2
COMMENTS
If a(5) exists, it must be a square bigger than 3*10^8.
Conjecture: 2 and 9 are the only numbers n such that 2n - 1, 2n + 1 and sigma(n) are all primes.
From Hiroaki Yamanouchi, Nov 19 2014: (Start)
a(n) (n >= 3) must be of the form 3^(2k) for some positive integer k.
(End)
EXAMPLE
Number 729 is in the sequence because 2*729 + 1 = 1459 and sigma(729) = 1093 (both primes).
MATHEMATICA
Join[{1}, Select[Range[0, 1000], PrimeQ[DivisorSigma[1, #]]&& PrimeQ[2 # + 1] &]] (* Vincenzo Librandi, Nov 14 2014 *)
Join[{1}, Select[Range[1000], AllTrue[{2#+1, DivisorSigma[1, #]}, PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 06 2019 *)
PROG
(Magma) [1] cat [n: n in [1..10000000] | IsPrime(2*n+1) and IsPrime(SumOfDivisors(n))]; // corrected by Vincenzo Librandi, Nov 14 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Nov 14 2014
STATUS
approved