OFFSET
1,3
COMMENTS
a(27) > 1.5*10^6. - Matthias Baur, Jan 16 2020
a(20) > 2*10^5. - Robert Price, Nov 23 2013
Primes resulting from a(1)-a(19) are confirmed primes (not probable primes) using BLS (N-1/N+1) test in pfgw. - Robert Price, Nov 23 2013
From Matthias Baur, Jan 16 2020: (Start)
Double checked to n=2*10^5, tested further to n=1.5*10^6 using the sieve programs newpgen and srsieve and using Jean Penné's LLR application (BLS (N-1/N+1) test).
a(20) was already known in 2005, but was not listed here until 2018 (see Prime Pages link). (End)
Because of the factorization 4*x^4 + 1 = (2*x^2 - 2*x + 1)*(2*x^2 + 2*x + 1), the only term divisible by 4 is 0. - Jeppe Stig Nielsen, Sep 12 2024
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
C. K. Caldwell, The Prime Pages
Douglas E. Iannucci, Deng Moujie and Graeme L. Cohen, On Perfect Totient Numbers, J. Integer Sequences, 6 (2003), #03.4.5.
P. Loomis, M. Plytage and J. Polhill, Summing up the Euler 'phi' function, The College Mathematics Journal, vol. 39 (2008), pp. 34-42.
H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2*3^n+1 and 2*3^n-1, Math. Comp., 26 (1972), 995-998.
MATHEMATICA
a[n_]:=If[PrimeQ[4*3^n + 1 ], n]; DeleteCases[Array[a, 40, 0], Null] (* Stefano Spezia, Nov 12 2018 *)
PROG
(PARI) is_a(m) = isprime(4*3^m + 1) \\ Michel Marcus, Jul 12 2013
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(15)-a(17) from Douglas Burke (dburke(AT)nevada.edu)
a(18) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Jan 26 2004
a(19) from Robert Price, Nov 23 2013
a(20)-a(21) from Matthias Baur, Nov 07 2018
a(22) from Matthias Baur, Dec 06 2018
a(23)-a(24) from Matthias Baur, Jul 23 2019
a(25) from Matthias Baur, Dec 07 2019
a(26) from Matthias Baur, Jan 16 2020
a(27)-a(29) from Ryan Propper, May 08 2020
STATUS
approved