OFFSET
1,1
COMMENTS
Interprimes are in A024675, even interprimes are in A072568, odd interprimes are in A072569 n^2 as interprimes are in A075190, 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, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
EXAMPLE
4 is a term because 4^3 = 64 is the average of two successive primes 61 and 57.
MAPLE
s := 3: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
MATHEMATICA
Select[ Range[548], 2#^3 == PrevPrim[ #^3] + NextPrim[ #^3] &]
n3ipQ[n_]:=Mean[{NextPrime[n^3], NextPrime[n^3, -1]}]==n^3; Select[ Range[ 600], n3ipQ] (* Harvey P. Dale, Oct 05 2017 *)
Select[Surd[Mean[#], 3]&/@Partition[Prime[Range[8*10^6]], 2, 1], IntegerQ] (* Harvey P. Dale, Apr 07 2023 *)
PROG
(PARI) is(n)=n=n^3; nextprime(n)+precprime(n)==2*n \\ Charles R Greathouse IV, Aug 25 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 09 2002
EXTENSIONS
Edited by Robert G. Wilson v Sep 14 2002
STATUS
approved