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A075229
Numbers k such that k^6 is an interprime = average of two successive primes.
10
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
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
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] &]
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 09 2002
EXTENSIONS
Edited by Robert G. Wilson v Sep 14 2002
STATUS
approved