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

1,1

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

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

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

Sequence in context: A073687 A187084 A090818 * A320922 A028594 A239050

Adjacent sequences: A075188 A075189 A075190 * A075192 A075193 A075194

Keyword

nonn

Author

Zak Seidov, Sep 09 2002

Extensions

Edited by Robert G. Wilson v Sep 14 2002

Status

approved