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A075234 Least k such that k^n is the smallest interprime which is an n-th power. 10
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 (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^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.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..100 (large primes well may be only pseudoprimes)

EXAMPLE

a(1)=4 because 4^1 = 4 is the smallest interprime of the form a^1, a(2)=2 because 2^2 = 4 is the smallest interprime of the form a^2, a(3)=4 because 4^3 = 64 is the smallest interprime of the form a^3, a(5)=20 because 20^5 = 3200000 is the smallest interprime of the form a^5. a(29)=315 because 315^29 =  2824919391960653953906106164519699385714864156233560852706432342529296875 is the smallest interprime of the form a^29.

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

CROSSREFS

Cf. A024675, A072568, A072569, A075190-A075192, A075228-A075234.

The first 10 terms in this sequence are the first terms in A024675, A075190-A075192, A075228-A075233.

Sequence in context: A038702 A085062 A053051 * A232715 A317951 A095382

Adjacent sequences:  A075231 A075232 A075233 * A075235 A075236 A075237

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 09 2002

EXTENSIONS

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

Typos in EXAMPLE fixed by Zak Seidov, Feb 09 2012

STATUS

approved

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)