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%I #18 May 25 2021 08:08:41
%S 12,111,116,175,183,205,246,305,313,406,438,593,594,620,696,714,788,
%T 824,844,969,1014,1023,1061,1080,1153,1176,1204,1288,1367,1456,1470,
%U 1515,1533,1538,1572,1626,1659,1689,1692,1695,1734,1759,1788,1860,1928
%N Numbers k such that k^8 is an interprime = average of two successive primes.
%C 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^7 as interprimes are in A075230, 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 Amiram Eldar, <a href="/A075231/b075231.txt">Table of n, a(n) for n = 1..10000</a>
%e 12 is a term because 12^8 = 429981696 is the average of two successive primes 429981691 and 429981701.
%p s := 8: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%t Select[Range[2000], 2#^8 == NextPrime[#^8, -1] + NextPrime[#^8] &]
%Y Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y Cf. A075228, A075229, A075230, A075232, A075233, A075234.
%K nonn
%O 1,1
%A _Zak Seidov_, Sep 09 2002
%E Edited by _Robert G. Wilson v_ Sep 14 2002
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