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A178700 Lonely primes between two consecutive nontrivial powers. 0
127, 223, 251, 64007, 1295033, 2535525373, 542939080319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

While the number of perfect powers < n is ~ sqrt(n) and the number of primes < n is ~ n/log(n), this does not preclude more terms from existing, but it does make it very unlikely. [Robert G. Wilson v, Jun 10 2010]

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

5^3 < 127 < 2^7;

6^3 < 223 < 15^2;

3^5 < 251 < 2^8;

40^3 < 64007 < 253^2;

109^3 < 1295033 < 1138^2.

From Carlos Rivera, Tue Nov 26 2013: (Start)

50354^2 < 2535525373 < 76^5;

8158^3 < 542939080319 < 736844^2. (End)

MATHEMATICA

nextPerfectPower[n_] := Block[{k = n + 1}, While[ GCD @@ Last /@ FactorInteger@k == 1, k++ ]; k]; a = 1; b = 3; lst = {}; While[a < 15 10^8, If[ PrimePi@b == 1 + PrimePi@a, p = NextPrime@a; AppendTo[lst, p]; Print@p]; a = b; b = nextPerfectPower@b]; lst (* Robert G. Wilson v, Jun 10 2010 *)

CROSSREFS

Sequence in context: A276261 A343319 A045117 * A142466 A268860 A142491

Adjacent sequences:  A178697 A178698 A178699 * A178701 A178702 A178703

KEYWORD

nonn

AUTHOR

Marot Alain (marot.alain(AT)orange.fr), Jun 05 2010

EXTENSIONS

First 5 terms checked by Robert G. Wilson v, Jun 10 2010

a(6) - a(7) from Carlos Rivera, Tue Nov 26 2013

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)