A005538 Numbers n such that 8*3^n + 1 is prime.

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

Author

N. J. A. Sloane

Keywords

• nonn
• hard

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

• Prime Wiki, General Proth prime of the form 8*3^n+1
• 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.

Crossrefs

Cf. A056799.

Programs

Mathematica

Select[Range[5000], PrimeQ[8*3^# + 1] &] (* Michael De Vlieger, Jun 26 2017 *)

PARI

v=[ ]; for(n=0,2000, if(isprime(8*3^n+1),v=concat(v,n),)); v

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