OFFSET
1,1
COMMENTS
Interprimes are in A024675, even interprimes are in A072568, odd interprimes are in A072569 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, 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..1317 from Zak Seidov)
FORMULA
a(n) = sqrt(A069495(n)).
EXAMPLE
3 is a term because 3^2 = 9 is the average of two successive primes 7 and 11.
MAPLE
s := 2: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;
MATHEMATICA
PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Select[ Range[464], 2#^2 == PrevPrim[ #^2] + NextPrim[ #^2] &] (* Robert G. Wilson v, Sep 14 2002 *)
n2ipQ[n_]:=Module[{n2=n^2}, (NextPrime[n2]+NextPrime[n2, -1])/2==n2]; Select[Range[500], n2ipQ] (* Harvey P. Dale, May 04 2011 *)
Select[Sqrt[Mean[#]]&/@Partition[Prime[Range[30000]], 2, 1], IntegerQ] (* Harvey P. Dale, May 26 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 09 2002
EXTENSIONS
Edited by Robert G. Wilson v, Sep 14 2002
STATUS
approved