A239713 Primes of the form m = 3^i + 3^j - 1, where i > j >= 0.

3, 11, 29, 83, 89, 107, 251, 269, 809, 971, 2213, 2267, 6563, 6569, 6803, 8747, 19709, 19763, 20411, 59051, 65609, 177173, 183707, 531521, 538001, 590489, 1594331, 1594403, 1595051, 1596509, 4782971, 4782977, 4783697, 14348909, 14349149, 14526053, 14880347

Offset

1,1

Comments

The base-3 representation of a term 3^i + 3^j - 1 has base-3 digital sum = 1 + 2*j == 1 (mod 2).

In base-3 representation the first terms are 10, 102, 1002, 10002, 10022, 10222, 100022, 100222, 1002222, 1022222, 10000222, 10002222, 100000002, 100000022, 100022222, 102222222, 1000000222, 1000002222, 1000222222, 10000000002, 10022222222, 100000000222, 100022222222, ...

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..131

Example

a(1) = 3, since 3 = 3^1 + 3^0 - 1 is prime.
a(5) = 89, since 89 = 3^4 + 3^2 - 1 is prime.

Prog

(Smalltalk)
A239713
"Answers the n-th term of A239713.
  Usage: n A239713
  Answer: a(n)"
  | a b i j k p q terms |
  terms := OrderedCollection new.
  k := 0.
  b := 3.
  p := b.
  i := 1.
  [k < self] whileTrue:
         [j := 0.
         q := 1.
         [j < i and: [k < self]] whileTrue:
                   [a := p + q - 1.
                   a isPrime
                        ifTrue:
                            [k := k + 1.
                            terms add: a].
                   q := b * q.
                   j := j + 1].
         i := i + 1.
         p := b * p].
     ^terms at: self
[by Hieronymus Fischer, Apr 14 2014]
--------------------
(Smalltalk)
A239713
"Version 2: Answers the n-th term of A239713.
  Uses distinctPowersOf: b from A018900
  Usage: n A239713
  Answer: a(n)”
  | a k n terms |
  terms := OrderedCollection new.
  n := 1.
  k := 0.
  [k < self] whileTrue:
         [(a:= (n distinctPowersOf: 3) - 1)
              isPrime ifTrue:    [k := k + 1.
                                 terms add: a].
              n := n + 1].
  ^terms at: self
[by Hieronymus Fischer, Apr 22 2014]
-----------
(Smalltalk)
A239713
  "Version 3: Answer an array of the first n terms of A239713.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
  Usage: n A239713
  Answer: #(3 11 29 ... ) [a(1) ... a(n)]”
  ^self primesWhichAreDistinctPowersOf: 3 withOffset: -1
[by Hieronymus Fischer, Apr 22 2014]

Crossrefs

Cf. A239709, A239712 - A239720.

Sequence in context: A110954 A000251 A159229 * A122023 A259594 A293010

Adjacent sequences: A239710 A239711 A239712 * A239714 A239715 A239716

Keyword

nonn

Author

Hieronymus Fischer, Mar 28 2014

Status

approved