OFFSET
1,1
COMMENTS
Roger Horn computed the first 776 terms of this sequence around 1961 to test (with Paul Bateman) their conjecture on the density of simultaneous primes in polynomials. - Charles R Greathouse IV, Apr 05 2011
Starting with a(3)=5 all terms are of the form 6k-1, k in A147683. - Zak Seidov, Nov 10 2008
Primes p such that the sum of divisors of p^2 (sigma(p^2) = A000203(p^2) = p^2+p+1) is prime. - Claudio Meller, Apr 07 2011
The generated prime numbers p^2 + p + 1 are exactly A053183. - Bernard Schott, Dec 20 2012
Positive squarefree k such that the sum of divisors of k^2 is prime. - Peter Munn, Feb 02 2018
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 2650 terms from M. F. Hasler).
Paul T. Bateman and Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962), 363-367.
Paolo Santonastaso and Ferdinando Zullo, Linearized trinomials with maximum kernel, arXiv:2012.14861 [math.NT], 2020.
MATHEMATICA
Select[Prime[Range[427]], PrimeQ[#^2+#+1]&] (* Bruno Berselli, Nov 08 2011 *)
PROG
(PARI) isA053182(n)=isprime(n) && isprime(n^2+n+1) \\ Michael B. Porter, Apr 23 2010
(PARI) c=0; forprime(p=1, default(primelimit), isprime(p^2+p+1) & write("/tmp/b053182.txt", c++, " "p)) \\ M. F. Hasler, Apr 07 2011
(Magma) [p: p in PrimesUpTo(10000) | IsPrime(p^2+p+1)]; // Vincenzo Librandi, Aug 06 2010
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Enoch Haga, Mar 01 2000
EXTENSIONS
List changed to cross-reference by Franklin T. Adams-Watters, May 12 2010
STATUS
approved