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%I #26 May 25 2021 08:09:00
%S 4,2,4,3,20,2,20,12,9,9,24,2,23,26,20,66,10,3,16,3,92,13,18,48,230,
%T 129,78,181,315,33,231,19,14,152,78,39,39,4,144,9,143,55,106,25,10,91,
%U 17,7,107,91,35,44,426,81,380,97,265,237,611,1034,122,1072,298,1213,18,51
%N Least k such that k^n is the smallest interprime which is an n-th power.
%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^8 as interprimes are in A075231, n^9 as interprimes are in A075232, n^10 as interprimes are in A075233.
%H Amiram Eldar, <a href="/A075234/b075234.txt">Table of n, a(n) for n = 1..250</a> (terms 1..100 from Zak Seidov)
%e a(1)=4 because 4^1 = 4 is the smallest interprime of the form k^1.
%e a(2)=2 because 2^2 = 4 is the smallest interprime of the form k^2.
%e a(3)=4 because 4^3 = 64 is the smallest interprime of the form k^3.
%e a(5)=20 because 20^5 = 3200000 is the smallest interprime of the form k^5.
%e a(29)=315 because 315^29 is the smallest interprime of the form k^29.
%p s := 10: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
%t PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {}; Do[k = 2; While[2k^n != PrevPrim[k^n] + NextPrim[k^n], k++ ]; a = Append[a, k], {n, 1, 67}]; a
%Y Cf. A072568, A072569.
%Y The first 10 terms in this sequence are the first terms in A024675, A075190, A075191, A075192, A075228, A075229, A075230, A075231, A075232, A075233.
%K nonn
%O 1,1
%A _Zak Seidov_, Sep 09 2002
%E Edited and extended by _Robert G. Wilson v_, Sep 14 2002
%E Typos in EXAMPLE fixed by _Zak Seidov_, Feb 09 2012
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