A075232 Numbers k such that k^9 is an interprime = average of two successive primes.

9, 74, 110, 141, 340, 370, 411, 423, 546, 687, 720, 723, 725, 744, 813, 834, 966, 1033, 1054, 1137, 1178, 1233, 1264, 1284, 1287, 1320, 1335, 1460, 1636, 1642, 1768, 1934, 2046, 2053, 2064, 2103, 2214, 2397, 2447, 2465, 2486, 2496, 2510, 2716, 2741, 2775

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^6 as interprimes are in A075229, n^7 as interprimes are in A075230, n^8 as interprimes are in A075231, 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

9 is a term because 9^9 = 387420489 is the average of two successive primes 387420479 and 387420499.

Maple

s := 9: 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[2869], 2#^9 == NextPrime[#^9, -1] + NextPrime[#^9] &]

Crossrefs

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

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

Sequence in context: A015465 A144782 A218872 * A145524 A319961 A037533

Adjacent sequences: A075229 A075230 A075231 * A075233 A075234 A075235

Keyword

nonn

Author

Zak Seidov, Sep 09 2002

Extensions

Edited by Robert G. Wilson v Sep 14 2002

Status

approved