A075191 Numbers k such that k^3 is an interprime = average of two successive primes.

4, 12, 16, 26, 28, 36, 48, 58, 66, 68, 74, 78, 102, 106, 112, 117, 124, 126, 129, 130, 148, 152, 170, 174, 184, 189, 190, 192, 224, 273, 280, 297, 321, 324, 369, 372, 373, 399, 408, 410, 421, 426, 429, 435, 447, 449, 450, 470, 475, 496, 504, 507, 531, 537

Offset: 1

Author

Zak Seidov, Sep 09 2002

Keywords

• nonn

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.

Examples

			4 is a term because 4^3 = 64 is the average of two successive primes 61 and 57.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)

Crossrefs

Cf. A024675, A072568, A072569, A075190, A075192.

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

Programs

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 *)

PARI

is(n)=n=n^3;nextprime(n)+precprime(n)==2*n \\ Charles R Greathouse IV, Aug 25 2014

Extensions

Edited by Robert G. Wilson v Sep 14 2002