A239717 - OEIS

%I #14 Aug 13 2023 15:53:30

%S 7,349,19207,117991,120049,823591,5765143,5882449,6588343,40353949,

%T 282475591,2017680349,2259801991,13841289601,14123762449,96894775207,

%U 96929364013,678223072897,678223075249,4747567274743,5425784582791

%N Primes of the form m = 7^i + 7^j - 1, where i > j >= 0.

%C The base-7 representation of a term 7^i + 7^j - 1 has base-7 digital sum = 1 + 6*j == 1 (mod 6).

%C 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.

%H Hieronymus Fischer, <a href="/A239717/b239717.txt">Table of n, a(n) for n = 1..40</a>

%e a(1) = 7, since 7 = 7^1 + 7^0 - 1 is prime.

%e a(2) = 349, since 349 = 7^3 + 7^1 - 1 is prime.

%t Select[Flatten[Table[7^x+7^y-1,{x,0,20},{y,0,x-1}]],PrimeQ] (* _Harvey P. Dale_, Aug 13 2023 *)

%o (Smalltalk)

%o A239717

%o   "Answers an array of the first n terms of A239717.

%o   Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.

%o   Usage: n A239717

%o   Answer: #(7 349 ... ) [a(1) ... a(n)]"

%o   ^self primesWhichAreDistinctPowersOf: 7 withOffset: -1

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Apr 14 2014