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A296422 Primes that can be represented in the form b^n+1 or b^n-1 where b >= 2 and n >= 2.

%I A296422 #39 Jan 08 2018 21:01:50
%S A296422 3,5,7,17,31,37,101,127,197,257,401,577,677,1297,1601,2917,3137,4357,
%T A296422 5477,7057,8101,8191,8837,12101,13457,14401,15377,15877,16901,17957,
%U A296422 21317,22501,24337,25601,28901,30977,32401,33857,41617,42437,44101,50177,52901
%N A296422 Primes that can be represented in the form b^n+1 or b^n-1 where b >= 2 and n >= 2.
%C A296422 Union of A000668 and A121326. - _Andrey Zabolotskiy_, Dec 21 2017
%H A296422 Robert Israel, <a href="/A296422/b296422.txt">Table of n, a(n) for n = 1..10000</a>
%p A296422 N:= 10^5: # to get terms <= N
%p A296422 R:= 3:
%p A296422 for b from 2 while b^2+1 <= N do
%p A296422   p:= 2:
%p A296422   do
%p A296422     p:= nextprime(p);
%p A296422     if b^p-1 > N then break fi;
%p A296422     if isprime(b^p-1) then R:= R, b^p-1 fi;
%p A296422   od:
%p A296422   p:= 1:
%p A296422   do
%p A296422     p:= 2*p;
%p A296422     if b^p+1 > N then break fi;
%p A296422     if isprime(b^p+1) then R:= R, b^p+1 fi;
%p A296422   od;
%p A296422 od:
%p A296422 sort(convert({R},list)); # _Robert Israel_, Jan 08 2018
%t A296422 Select[Prime@ Range[2, 10^4], AnyTrue[# + {-1, 1}, Or[# == 1, GCD @@ FactorInteger[#][[All, -1]] > 1] &] &] (* _Michael De Vlieger_, Dec 13 2017 *)
%o A296422 (PARI) lista(nn) = {forprime(p=2, nn, if ((p==2) || ispower(p+1) || ispower(p-1), print1(p, ", ")); ); } \\ _Michel Marcus_, Dec 13 2017
%Y A296422 Cf. A000040 (primes), A001597 (perfect powers).
%Y A296422 Cf. A000668 (Mersenne primes), A121326.
%K A296422 nonn
%O A296422 1,1
%A A296422 _Nathaniel J. Strout_, Dec 12 2017