A075229 - OEIS

A075229

Numbers k such that k^6 is an interprime = average of two successive primes.

2, 4, 6, 18, 24, 27, 30, 53, 96, 122, 175, 195, 213, 231, 265, 300, 408, 420, 426, 450, 492, 532, 570, 614, 618, 657, 682, 705, 774, 777, 822, 858, 915, 946, 948, 1001, 1008, 1061, 1073, 1107, 1145, 1186, 1233, 1269, 1323, 1352, 1374, 1406, 1413, 1440, 1480

(list; graph; refs; listen; history; text; internal format)

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^3 as interprimes are in A075191, n^4 as interprimes are in A075192, n^5 as interprimes are in A075228, 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

EXAMPLE

2 is a term because 2^6 = 64 is the average of two successive primes 63 and 67.

MAPLE

s := 6: 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[1500], 2#^6 == NextPrime[#^6, -1] + NextPrime[#^6] &]

CROSSREFS

Cf. A024675, A072568, A072569, A075190, A075191, A075192.

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

Sequence in context: A019464 A064402 A268577 * A242765 A073664 A088174