cp's OEIS Frontend

A165701 Numbers n such that 5^n-6 is prime.

%I A165701 #14 Jun 13 2017 10:21:01
%S A165701 2,4,5,6,10,53,76,82,88,242,247,473,586,966,1015,1297,1825,2413,2599,
%T A165701 2833,5850,5965,6052,27199,49704,79000
%N A165701 Numbers n such that 5^n-6 is prime.
%C A165701 Numbers corresponding to the a(n) for n>11 are probable prime.
%C A165701 If Q is a 4-perfect number and gcd(Q, 5*(5^a(n)-6))=1 then m=5^(a(n)-1)
%C A165701 (5^a(n)-6)*Q is a solution of the equation sigma(x)=5(x+Q)(see comment lines of the sequence A058959). 142990848 is the smallest 4-perfect number m such that 5 doesn't divide m.
%C A165701 a(27) > 10^5. - _Robert Price_, Feb 03 2014
%H A165701 F. Firoozbakht, M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1
%H A165701 H. Lifchitz, R. Lifchitz: PRP Top Records <a href="http://www.primenumbers.net/prptop/searchform.php?form=5^n-6&amp;action=Search">Search for 5^n-6</a>.
%t A165701 Do[If[PrimeQ[5^n-6],Print[n]],{n,8888}]
%o A165701 (PARI) is(n)=ispseudoprime(5^n-6) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A165701 Cf. A007691, A054030, A058959.
%K A165701 more,nonn
%O A165701 1,1
%A A165701 M. F. Hasler and _Farideh Firoozbakht_, Oct 30 2009
%E A165701 a(24)-a(26) from _Robert Price_, Feb 03 2014