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A075228 Numbers k such that k^5 is an interprime = average of two successive primes.

%I A075228 #18 May 25 2021 08:08:25
%S A075228 20,42,77,81,186,198,200,220,248,266,270,294,300,387,411,477,498,537,
%T A075228 630,678,682,696,728,741,774,819,872,985,987,1001,1014,1037,1060,1083,
%U A075228 1084,1087,1098,1140,1155,1162,1232,1245,1278,1316,1370,1392,1397,1402
%N A075228 Numbers k such that k^5 is an interprime = average of two successive primes.
%C A075228 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^6 as interprimes are in A075229, 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 A075228 Amiram Eldar, <a href="/A075228/b075228.txt">Table of n, a(n) for n = 1..10000</a>
%e A075228 20 is a term because 20^5 = 3200000 is the average of two successive primes 3199997 and 3200003.
%p A075228 s := 5: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%Y A075228 Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y A075228 Cf. A075229, A075230, A075231, A075232, A075233, A075234.
%K A075228 nonn
%O A075228 1,1
%A A075228 _Zak Seidov_, Sep 09 2002
%E A075228 More terms from _Jason Earls_, Sep 09 2002
%E A075228 Edited by _Robert G. Wilson v_ Sep 14 2002