A116086 Perfect powers n with no primes between n and the next larger perfect power, which is in A116455.

8, 25, 32, 121, 2187, 3125, 32761, 79507, 97336, 503284356

Offset

1,1

Comments

No other n<10^12. There is a conjecture that this sequence is finite.

No other terms < 10^18. - Jud McCranie, Nov 03 2013

No other terms < 4.5*10^18. - Giovanni Resta, Apr 28 2014

Links

Table of n, a(n) for n=1..10.

March 2006 NMBRTHRY Archives

Wikipedia, Redmond-Sun conjecture

Example

The prime-free ranges are (2^3,3^2), (5^2,3^3), (2^5,6^2), (11^2,5^3), (3^7,13^3), (5^5,56^2), (181^2,2^15), (43^3,282^2), (46^3,312^2), (22434^2,55^5).

Mathematica

lim=10^12; lst={}; k=2; While[n=Floor[lim^(1/k)]; n>=2, lst=Join[lst, Range[2, n]^k]; k++ ]; lst=Union[lst]; PrimeFree[n1_, n2_] := Module[{n=n1+1}, While[n<n2&&!PrimeQ[n], n++ ]; n ==n2]; lst2={}; Do[If[PrimeFree[lst[[i]], lst[[i+1]]], AppendTo[lst2, lst[[i]]]], {i, Length[lst]-1}]; lst2

Crossrefs

Cf. A001597 (perfect powers), A116455.

Cf. A068435 (for prime powers).

Sequence in context: A030796 A266927 A240591 * A270739 A239582 A239583

Adjacent sequences: A116083 A116084 A116085 * A116087 A116088 A116089

Keyword

hard,nonn

Author

T. D. Noe, Mar 28 2006

Status

approved