A075233 Numbers k such that k^10 is an interprime = average of two successive primes.

9, 42, 87, 105, 108, 141, 144, 166, 215, 250, 381, 387, 482, 490, 500, 645, 748, 792, 831, 860, 876, 968, 990, 1377, 1448, 1468, 1526, 1769, 1780, 1922, 1968, 2084, 2118, 2228, 2245, 2252, 2373, 2381, 2478, 2565, 2672, 2781, 2883, 2915, 2972, 2988, 3008

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^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^9 as interprimes are in A075232, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.

Examples

			9 is a term because 9^10 = 3486784401 is the average of two successive primes 3486784393 and 3486784409.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

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

Programs

Maple

s := 10: 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[3087], 2#^10 == NextPrime[#^10, -1] + NextPrime[#^10] &]
Select[Range[3100],With[{c=#^10},c==Mean[{NextPrime[c],NextPrime[c,-1]}]]&] (* Harvey P. Dale, May 21 2025 *)

Extensions

Edited by Robert G. Wilson v Sep 14 2002