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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 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.)