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)
"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)
"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)
"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
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Mar 28 2014
STATUS
approved