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A239717 Primes of the form m = 7^i + 7^j - 1, where i > j >= 0.

%I A239717 #14 Aug 13 2023 15:53:30
%S A239717 7,349,19207,117991,120049,823591,5765143,5882449,6588343,40353949,
%T A239717 282475591,2017680349,2259801991,13841289601,14123762449,96894775207,
%U A239717 96929364013,678223072897,678223075249,4747567274743,5425784582791
%N A239717 Primes of the form m = 7^i + 7^j - 1, where i > j >= 0.
%C A239717 The base-7 representation of a term 7^i + 7^j - 1 has base-7 digital sum = 1 + 6*j == 1 (mod 6).
%C A239717 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 A239717 Hieronymus Fischer, <a href="/A239717/b239717.txt">Table of n, a(n) for n = 1..40</a>
%e A239717 a(1) = 7, since 7 = 7^1 + 7^0 - 1 is prime.
%e A239717 a(2) = 349, since 349 = 7^3 + 7^1 - 1 is prime.
%t A239717 Select[Flatten[Table[7^x+7^y-1,{x,0,20},{y,0,x-1}]],PrimeQ] (* _Harvey P. Dale_, Aug 13 2023 *)
%o A239717 (Smalltalk)
%o A239717 A239717
%o A239717   "Answers an array of the first n terms of A239717.
%o A239717   Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
%o A239717   Usage: n A239717
%o A239717   Answer: #(7 349 ... ) [a(1) ... a(n)]"
%o A239717   ^self primesWhichAreDistinctPowersOf: 7 withOffset: -1
%K A239717 nonn
%O A239717 1,1
%A A239717 _Hieronymus Fischer_, Apr 14 2014