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

2, 4, 5, 6, 10, 53, 76, 82, 88, 242, 247, 473, 586, 966, 1015, 1297, 1825, 2413, 2599, 2833, 5850, 5965, 6052, 27199, 49704, 79000

Offset

1,1

Comments

Numbers corresponding to the a(n) for n>11 are probable prime.

If Q is a 4-perfect number and gcd(Q, 5*(5^a(n)-6))=1 then m=5^(a(n)-1)

(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.

a(27) > 10^5. - Robert Price, Feb 03 2014

Links

Table of n, a(n) for n=1..26.

F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1

H. Lifchitz, R. Lifchitz: PRP Top Records Search for 5^n-6.

Mathematica

Do[If[PrimeQ[5^n-6], Print[n]], {n, 8888}]

Prog

(PARI) is(n)=ispseudoprime(5^n-6) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A007691, A054030, A058959.

Sequence in context: A101964 A294812 A217354 * A129305 A278507 A113631

Adjacent sequences: A165698 A165699 A165700 * A165702 A165703 A165704

Keyword

more,nonn

Author

M. F. Hasler and Farideh Firoozbakht, Oct 30 2009

Extensions

a(24)-a(26) from Robert Price, Feb 03 2014

Status

approved