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A075229 Numbers k such that k^6 is an interprime = average of two successive primes.

%I A075229 #17 May 25 2021 08:08:35
%S A075229 2,4,6,18,24,27,30,53,96,122,175,195,213,231,265,300,408,420,426,450,
%T A075229 492,532,570,614,618,657,682,705,774,777,822,858,915,946,948,1001,
%U A075229 1008,1061,1073,1107,1145,1186,1233,1269,1323,1352,1374,1406,1413,1440,1480
%N A075229 Numbers k such that k^6 is an interprime = average of two successive primes.
%C A075229 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^7 as interprimes are in A075230, 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 A075229 Amiram Eldar, <a href="/A075229/b075229.txt">Table of n, a(n) for n = 1..10000</a>
%e A075229 2 is a term because 2^6 = 64 is the average of two successive primes 63 and 67.
%p A075229 s := 6: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%t A075229 Select[Range[1500], 2#^6 == NextPrime[#^6,-1] + NextPrime[#^6] &]
%Y A075229 Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y A075229 Cf. A075228, A075230, A075231, A075232, A075233, A075234.
%K A075229 nonn
%O A075229 1,1
%A A075229 _Zak Seidov_, Sep 09 2002
%E A075229 Edited by _Robert G. Wilson v_ Sep 14 2002