|
|
A239717
|
|
Primes of the form m = 7^i + 7^j - 1, where i > j >= 0.
|
|
1
|
|
|
7, 349, 19207, 117991, 120049, 823591, 5765143, 5882449, 6588343, 40353949, 282475591, 2017680349, 2259801991, 13841289601, 14123762449, 96894775207, 96929364013, 678223072897, 678223075249, 4747567274743, 5425784582791
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The base-7 representation of a term 7^i + 7^j - 1 has base-7 digital sum = 1 + 6*j == 1 (mod 6).
Numbers m that satisfy m = 7^i + 7^j + 1 are never primes, since the base-7 digital sum of m is 3, and thus, m is divisible by 3.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 7, since 7 = 7^1 + 7^0 - 1 is prime.
a(2) = 349, since 349 = 7^3 + 7^1 - 1 is prime.
|
|
MATHEMATICA
|
Select[Flatten[Table[7^x+7^y-1, {x, 0, 20}, {y, 0, x-1}]], PrimeQ] (* Harvey P. Dale, Aug 13 2023 *)
|
|
PROG
|
(Smalltalk)
"Answers an array of the first n terms of A239717.
Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
Answer: #(7 349 ... ) [a(1) ... a(n)]"
^self primesWhichAreDistinctPowersOf: 7 withOffset: -1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|