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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contribution 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

Also a member is 2*A056799(16) = 2*161930 = 323860, but I do not know if it is the next member. - Jeppe Stig Nielsen, Oct 13 2019

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..20.

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

Adjacent sequences:  A005535 A005536 A005537 * A005539 A005540 A005541

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Douglas Burke (dburke(AT)nevada.edu)

a(19)-a(20) from Robert Price, Mar 16 2014

STATUS

approved

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Last modified January 20 10:58 EST 2020. Contains 331081 sequences. (Running on oeis4.)