A075229 - OEIS

%I #17 May 25 2021 08:08:35

%S 2,4,6,18,24,27,30,53,96,122,175,195,213,231,265,300,408,420,426,450,

%T 492,532,570,614,618,657,682,705,774,777,822,858,915,946,948,1001,

%U 1008,1061,1073,1107,1145,1186,1233,1269,1323,1352,1374,1406,1413,1440,1480

%N Numbers k such that k^6 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^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 Amiram Eldar, <a href="/A075229/b075229.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 is a term because 2^6 = 64 is the average of two successive primes 63 and 67.

%p s := 6: 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[1500], 2#^6 == NextPrime[#^6,-1] + NextPrime[#^6] &]

%Y Cf. A024675, A072568, A072569, A075190, A075191, A075192.

%Y Cf. A075228, A075230, A075231, A075232, A075233, A075234.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 09 2002

%E Edited by _Robert G. Wilson v_ Sep 14 2002