login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005537 Numbers n such that 4*3^n + 1 is prime.
(Formerly M0803)
6
0, 1, 2, 3, 6, 14, 15, 39, 201, 249, 885, 1005, 1254, 1635, 3306, 3522, 9602, 19785, 72698, 233583, 328689, 537918 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(23) > 6*10^5. - Matthias Baur, Dec 06 2018

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

Double checked to n=2*10^5, tested further to n=6*10^5 using newpgen sieve program and Jean Penné's LLR application (BLS (N-1/N+1) test). - Matthias Baur, Dec 06 2018

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..22.

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) a(n) = isprime(4*3^n + 1) \\ Michel Marcus, Jul 12 2013

CROSSREFS

Sequence in context: A121556 A123041 A078557 * A282351 A193093 A182756

Adjacent sequences:  A005534 A005535 A005536 * A005538 A005539 A005540

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Chris K. Caldwell

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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 06:07 EST 2019. Contains 319323 sequences. (Running on oeis4.)