cp's OEIS Frontend

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

%I A005538 M1729 #67 Jul 06 2020 06:05:01
%S A005538 2,7,8,10,22,52,58,76,130,143,331,332,980,1282,1655,4031,4600,18880,
%T A005538 89482,130592,323860,872171,1172480
%N A005538 Numbers n such that 8*3^n + 1 is prime.
%C A005538 From _R. J. Mathar_, Mar 01 2010: (Start)
%C A005538 The row r=4 in the table of "Numbers n such that 2*r*3^n+1 is prime":
%C A005538 .1,..2,..4,..5,..6,..9,.16,.17,.30,.54,.57,.60,.65,.132,.180,
%C A005538 .1,..2,..3,..6,.14,.15,.39,201,249,
%C A005538 .1,..3,..4,..5,..8,.15,.16,.29,.53,.56,.59,.64,131,179,
%C A005538 .2,..7,..8,.10,.22,.52,.58,.76,130,143,
%C A005538 .1,..3,..4,..7,..9,.12,.18,.22,102,112,157,162,289,
%C A005538 .1,..2,..5,.13,.14,.38,200,248,
%C A005538 .1,..2,..3,.18,.22,.26,.27,.33,.39,.57,.62,.94,145,246,
%C A005538 .3,..4,..5,.12,.24,.36,.77,195,296,297,
%C A005538 .2,..3,..4,..7,.14,.15,.28,.52,.55,.58,.63,130,178,
%C A005538 .1,..2,..3,..4,..5,..8,.16,.19,.28,.50,134,280,
%C A005538 .1,..2,..4,..5,.10,.12,.14,.24,.34,.37,.52,.56,.65,.68,.96,106,128,156,169,236,254,
%C A005538 .1,..6,..7,..9,.21,.51,.57,.75,129,142,
%C A005538 .1,.12,.15,.17,.20,.29,.31,.32,.35,.37,.77,.95,193,203,224,296,
%C A005538 .3,..4,..8,.11,.14,.15,.18, (End)
%C A005538 a(21) > 2*10^5. - _Robert Price_, Mar 16 2014
%C A005538 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
%C A005538 a(22) > 8*10^5. - _Paul S. Vanderveen_, May 02 2020
%D A005538 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005538 Prime Wiki, <a href="https://www.rieselprime.de/ziki/Gen._Proth_prime_3_8">General Proth prime of the form 8*3^n+1</a>
%H A005538 H. C. Williams and C. R. Zarnke, <a href="http://www.jstor.org/stable/2005886">Some prime numbers of the forms 2*3^n+1 and 2*3^n-1</a>, Math. Comp., 26 (1972), 995-998.
%t A005538 Select[Range[5000], PrimeQ[8*3^# + 1] &] (* _Michael De Vlieger_, Jun 26 2017 *)
%o A005538 (PARI) v=[ ]; for(n=0,2000, if(isprime(8*3^n+1),v=concat(v,n),)); v
%Y A005538 Cf. A056799.
%K A005538 nonn,hard
%O A005538 1,1
%A A005538 _N. J. A. Sloane_
%E A005538 More terms from Douglas Burke (dburke(AT)nevada.edu)
%E A005538 a(19)-a(20) from _Robert Price_, Mar 16 2014
%E A005538 a(21) from _Paul S. Vanderveen_, Feb 09 2020
%E A005538 a(22) from _Paul S. Vanderveen_, Jun 12 2020
%E A005538 a(23) (found May 17 2020) from _Paul S. Vanderveen_, Jul 04 2020