A153090 Least k(n) such that k(n)*3^n*(3^n-1)+j is prime with j= -1 or 1 or both.

1, 1, 1, 1, 3, 1, 1, 14, 5, 5, 5, 1, 7, 6, 5, 7, 12, 1, 5, 1, 6, 29, 23, 20, 8, 6, 6, 9, 2, 10, 18, 19, 13, 57, 1, 1, 9, 10, 8, 5, 8, 8, 26, 5, 5, 6, 39, 41, 6, 9, 50, 6, 32, 6, 4, 8, 2, 79, 28, 23, 33, 78, 31, 35, 19, 32, 46, 7, 6, 116, 39, 7, 20, 6, 35, 8

Offset

1,5

Comments

Sum_{n=1..k} a(n) / Sum_{n=1..k} n tends to 2*log(3)/7.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

1*3^1*(3^1-1)-1=5 prime as 7 so k(1)=1 1*3^2*(3^2-1)-1=71 prime as 73 so k(2)=1

Mathematica

lk[n_]:=Module[{c=3^n (3^n-1), k=1}, While[NoneTrue[k*c+{1, -1}, PrimeQ], k++]; k]; Array[lk, 90] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 23 2020 *)

Crossrefs

Cf. A152414, A152091, A152092, A152093, A152094, A152095.

Sequence in context: A015112 A174690 A156869 * A203002 A073483 A006956

Adjacent sequences: A153087 A153088 A153089 * A153091 A153092 A153093

Keyword

nonn

Author

Pierre CAMI, Dec 18 2008

Extensions

Corrected by Harvey P. Dale, Dec 23 2020

Status

approved