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A075234
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Least k such that k^n is the smallest interprime which is an n-th power.
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10
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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; internal format)
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OFFSET
| 1,1
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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.
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LINKS
| Moshe Levin, Table of n, a(n) for n = 1..100 (large primes well may be only pseudoprimes)
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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.
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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;
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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
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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 * A095382 A135282 A179411
Adjacent sequences: A075231 A075232 A075233 * A075235 A075236 A075237
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KEYWORD
| nonn,changed
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 09 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 14 2002
Typos in EXAMPLE fixed by Moshe Levin (moshe.levin(AT)mail.ru), Feb 09 2012
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