This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178700 #13 Dec 19 2024 06:18:06
%S A178700 127,223,251,64007,1295033,2535525373,542939080319
%N A178700 Lonely primes between two consecutive nontrivial powers.
%C A178700 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]
%e A178700 5^3 < 127 < 2^7;
%e A178700 6^3 < 223 < 15^2;
%e A178700 3^5 < 251 < 2^8;
%e A178700 40^3 < 64007 < 253^2;
%e A178700 109^3 < 1295033 < 1138^2.
%e A178700 From _Carlos Rivera_, Nov 26 2013: (Start)
%e A178700 50354^2 < 2535525373 < 76^5;
%e A178700 8158^3 < 542939080319 < 736844^2. (End)
%t A178700 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 *)
%K A178700 nonn,more
%O A178700 1,1
%A A178700 Marot Alain (marot.alain(AT)orange.fr), Jun 05 2010
%E A178700 First 5 terms checked by _Robert G. Wilson v_, Jun 10 2010
%E A178700 a(6)-a(7) from _Carlos Rivera_, Nov 26 2013