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A005538
Numbers n such that 8*3^n + 1 is prime.
(Formerly M1729)
2
2, 7, 8, 10, 22, 52, 58, 76, 130, 143, 331, 332, 980, 1282, 1655, 4031, 4600, 18880, 89482, 130592, 323860, 872171, 1172480
OFFSET
1,1
COMMENTS
From R. J. Mathar, Mar 01 2010: (Start)
The row r=4 in the table of "Numbers n such that 2*r*3^n+1 is prime":
.1,..2,..4,..5,..6,..9,.16,.17,.30,.54,.57,.60,.65,.132,.180,
.1,..2,..3,..6,.14,.15,.39,201,249,
.1,..3,..4,..5,..8,.15,.16,.29,.53,.56,.59,.64,131,179,
.2,..7,..8,.10,.22,.52,.58,.76,130,143,
.1,..3,..4,..7,..9,.12,.18,.22,102,112,157,162,289,
.1,..2,..5,.13,.14,.38,200,248,
.1,..2,..3,.18,.22,.26,.27,.33,.39,.57,.62,.94,145,246,
.3,..4,..5,.12,.24,.36,.77,195,296,297,
.2,..3,..4,..7,.14,.15,.28,.52,.55,.58,.63,130,178,
.1,..2,..3,..4,..5,..8,.16,.19,.28,.50,134,280,
.1,..2,..4,..5,.10,.12,.14,.24,.34,.37,.52,.56,.65,.68,.96,106,128,156,169,236,254,
.1,..6,..7,..9,.21,.51,.57,.75,129,142,
.1,.12,.15,.17,.20,.29,.31,.32,.35,.37,.77,.95,193,203,224,296,
.3,..4,..8,.11,.14,.15,.18, (End)
a(21) > 2*10^5. - Robert Price, Mar 16 2014
2*A056799(16) = 2*161930 = 323860 is also a member, but I do not know if it is the next member. - Jeppe Stig Nielsen, Oct 13 2019
a(22) > 8*10^5. - Paul S. Vanderveen, May 02 2020
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
Select[Range[5000], PrimeQ[8*3^# + 1] &] (* Michael De Vlieger, Jun 26 2017 *)
PROG
(PARI) v=[ ]; for(n=0, 2000, if(isprime(8*3^n+1), v=concat(v, n), )); v
CROSSREFS
Cf. A056799.
Sequence in context: A075766 A258823 A226612 * A329648 A206331 A053013
KEYWORD
nonn,hard
EXTENSIONS
More terms from Douglas Burke (dburke(AT)nevada.edu)
a(19)-a(20) from Robert Price, Mar 16 2014
a(21) from Paul S. Vanderveen, Feb 09 2020
a(22) from Paul S. Vanderveen, Jun 12 2020
a(23) (found May 17 2020) from Paul S. Vanderveen, Jul 04 2020
STATUS
approved