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%I #16 May 25 2021 08:08:51
%S 9,74,110,141,340,370,411,423,546,687,720,723,725,744,813,834,966,
%T 1033,1054,1137,1178,1233,1264,1284,1287,1320,1335,1460,1636,1642,
%U 1768,1934,2046,2053,2064,2103,2214,2397,2447,2465,2486,2496,2510,2716,2741,2775
%N Numbers k such that k^9 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^8 as interprimes are in A075231, 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="/A075232/b075232.txt">Table of n, a(n) for n = 1..10000</a>
%e 9 is a term because 9^9 = 387420489 is the average of two successive primes 387420479 and 387420499.
%p s := 9: 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[2869], 2#^9 == NextPrime[#^9, -1] + NextPrime[#^9] &]
%Y Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y Cf. A075228, A075229, A075230, A075231, 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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