cp's OEIS Frontend

A075233 Numbers k such that k^10 is an interprime = average of two successive primes.

%I A075233 #18 May 21 2025 16:52:01
%S A075233 9,42,87,105,108,141,144,166,215,250,381,387,482,490,500,645,748,792,
%T A075233 831,860,876,968,990,1377,1448,1468,1526,1769,1780,1922,1968,2084,
%U A075233 2118,2228,2245,2252,2373,2381,2478,2565,2672,2781,2883,2915,2972,2988,3008
%N A075233 Numbers k such that k^10 is an interprime = average of two successive primes.
%C A075233 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, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.
%H A075233 Amiram Eldar, <a href="/A075233/b075233.txt">Table of n, a(n) for n = 1..10000</a>
%e A075233 9 is a term because 9^10 = 3486784401 is the average of two successive primes 3486784393 and 3486784409.
%p A075233 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 A075233 Select[Range[3087], 2#^10 == NextPrime[#^10, -1] + NextPrime[#^10] &]
%t A075233 Select[Range[3100],With[{c=#^10},c==Mean[{NextPrime[c],NextPrime[c,-1]}]]&] (* _Harvey P. Dale_, May 21 2025 *)
%Y A075233 Cf. A024675, A072568, A072569, A075190, A075191, A075192.
%Y A075233 Cf. A075228, A075229, A075230, A075231, A075232, A075234.
%K A075233 nonn
%O A075233 1,1
%A A075233 _Zak Seidov_, Sep 09 2002
%E A075233 Edited by _Robert G. Wilson v_ Sep 14 2002