A075190 Numbers k such that k^2 is an interprime = average of two successive primes.

2, 3, 8, 9, 12, 15, 18, 21, 25, 33, 41, 51, 60, 64, 72, 78, 92, 112, 117, 129, 138, 140, 159, 165, 168, 172, 192, 195, 198, 213, 216, 218, 228, 237, 273, 295, 298, 303, 304, 309, 322, 327, 330, 338, 342, 356, 360, 366, 387, 393, 408, 416, 429, 432, 441, 447, 456

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

Cf. A024675, A072568, A072569, A075191, A075192.

Cf. A075228, A075229, A075230, A075231, A075232, A075233, A075234.

Sequence in context: A283618 A284370 A273783 * A224225 A283160 A281148

Adjacent sequences: A075187 A075188 A075189 * A075191 A075192 A075193

Keyword

nonn

Author

Zak Seidov, Sep 09 2002

Extensions

Edited by Robert G. Wilson v, Sep 14 2002

Status

approved