cp's OEIS Frontend

A378364 Prime numbers such that the interval from the previous prime number contains a unique perfect power.

%I A378364 #18 Dec 18 2024 23:32:25
%S A378364 2,5,17,53,67,83,101,131,149,173,197,223,227,251,257,293,331,347,367,
%T A378364 401,443,487,521,541,577,631,677,733,787,853,907,967,1009,1031,1091,
%U A378364 1163,1229,1297,1361,1373,1447,1523,1601,1693,1733,1777,1861,1949,2027,2053
%N A378364 Prime numbers such that the interval from the previous prime number contains a unique perfect power.
%C A378364 Perfect-powers (A001597) are 1 and numbers with a proper integer root.
%e A378364 The prime before 17 is 13, and the interval (13,14,15,16,17) contains only one perfect power 16, so 17 is in the sequence.
%e A378364 The prime before 29 is 23, and the interval (23,24,25,26,27,28,29) contains two perfect powers 25 and 27, so 29 is not in the sequence.
%t A378364 perpowQ[n_]:=n==1||GCD@@FactorInteger[n][[All,2]]>1;
%t A378364 Select[Range[1000],PrimeQ[#]&&Length[Select[Range[NextPrime[#,-1],#],perpowQ]]==1&]
%Y A378364 For non prime powers we have A006512.
%Y A378364 For zero instead of one perfect power we have the prime terms of A345531.
%Y A378364 The indices of these primes are the positions of 1 in A377432.
%Y A378364 The indices of these primes are 1 + A377434(n-1).
%Y A378364 For more than one perfect power see A377466.
%Y A378364 Swapping "prime" with "perfect power" gives A378374.
%Y A378364 For next instead of previous prime we have A379154.
%Y A378364 A000040 lists the primes, differences A001223.
%Y A378364 A001597 lists the perfect powers, differences A053289.
%Y A378364 A007916 lists the non perfect powers, differences A375706.
%Y A378364 A081676 gives the greatest perfect power <= n.
%Y A378364 A377468 gives the least perfect power > n.
%Y A378364 Cf. A023055, A045542, A052410, A053607, A069623, A376560, A377287, A377436.
%K A378364 nonn
%O A378364 1,1
%A A378364 _Gus Wiseman_, Dec 16 2024