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A075230 Numbers k such that k^7 is an interprime = average of two successive primes.

%I A075230 #19 May 25 2021 08:08:30
%S A075230 20,33,41,71,82,99,151,165,254,267,283,316,345,462,486,496,516,630,
%T A075230 657,668,676,681,687,724,760,945,1004,1050,1085,1167,1305,1314,1316,
%U A075230 1326,1335,1389,1414,1420,1454,1456,1512,1638,1644,1726,1803,1874,1905,1963
%N A075230 Numbers k such that k^7 is an interprime = average of two successive primes.
%C A075230 Interprimes are in A024675, even interprimes are in A072568, odd interprimes are in A072569 n^2 as interprimes are in A075190, n^3 as interprimes are in A075191, n^4 as interprimes are in A075192, n^5 as interprimes are in A075228, n^6 as interprimes are in A075229, n^8 as interprimes are in A075231, n^9 as interprimes are in A075232, n^10 as interprimes are in A075233, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.
%H A075230 Amiram Eldar, <a href="/A075230/b075230.txt">Table of n, a(n) for n = 1..10000</a>
%e A075230 20 is a term because 20^7 = 1280000000 is the average of two successive primes 1279999997 and 1280000003.
%p A075230 s := 7: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%t A075230 Select[Range[2000],Mean[{NextPrime[#^7],NextPrime[#^7,-1]}]==#^7&] (* _Harvey P. Dale_, Aug 09 2013 *)
%Y A075230 Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y A075230 Cf. A075228, A075229, A075231, A075232, A075233, A075234.
%K A075230 nonn
%O A075230 1,1
%A A075230 _Zak Seidov_, Sep 09 2002
%E A075230 Edited by _Robert G. Wilson v_ Sep 14 2002