A075234 Least k such that k^n is the smallest interprime which is an n-th power.

4, 2, 4, 3, 20, 2, 20, 12, 9, 9, 24, 2, 23, 26, 20, 66, 10, 3, 16, 3, 92, 13, 18, 48, 230, 129, 78, 181, 315, 33, 231, 19, 14, 152, 78, 39, 39, 4, 144, 9, 143, 55, 106, 25, 10, 91, 17, 7, 107, 91, 35, 44, 426, 81, 380, 97, 265, 237, 611, 1034, 122, 1072, 298, 1213, 18, 51

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, n^10 as interprimes are in A075233.

Examples

			a(1)=4 because 4^1 = 4 is the smallest interprime of the form k^1.
a(2)=2 because 2^2 = 4 is the smallest interprime of the form k^2.
a(3)=4 because 4^3 = 64 is the smallest interprime of the form k^3.
a(5)=20 because 20^5 = 3200000 is the smallest interprime of the form k^5.
a(29)=315 because 315^29 is the smallest interprime of the form k^29.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..250 (terms 1..100 from Zak Seidov)

Crossrefs

Cf. A072568, A072569.

The first 10 terms in this sequence are the first terms in A024675, A075190, A075191, A075192, A075228, A075229, A075230, A075231, A075232, A075233.

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

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = {}; Do[k = 2; While[2k^n != PrevPrim[k^n] + NextPrim[k^n], k++ ]; a = Append[a, k], {n, 1, 67}]; a

Extensions

Edited and extended by Robert G. Wilson v, Sep 14 2002

Typos in EXAMPLE fixed by Zak Seidov, Feb 09 2012