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Perfect powers n such that (n-5)/2 is prime.
0

%I #8 Feb 24 2025 21:22:00

%S 9,27,2187,19683,300763,1092727,2048383,6128487,15069223,21717639,

%T 24642171,27818127,36264691,38958219,54439939,65450827,84604519,

%U 90224199,112678587,133432831,139798359,143055667,163667323,246491883,313046839,341532099,347428927

%N Perfect powers n such that (n-5)/2 is prime.

%e 9=3^2, 27=3^3, 2187=3^7, 19683=3^9, but 300763=67^3 - is there any rule?

%t pp = Join[{1}, Select[ Range[10^7], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[(# - 5)/2] & ]

%K easy,nonn,changed

%O 1,1

%A _Zak Seidov_, Oct 11 2002

%E Extended by _Robert G. Wilson v_, Oct 14 2002

%E More terms from _Sean A. Irvine_, Feb 24 2025