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A075190
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Numbers n such that n^2 is an interprime = average of two successive primes.
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18
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2, 3, 8, 9, 12, 15, 18, 21, 25, 33, 41, 51, 60, 64, 72, 78, 92, 112, 117, 129, 138, 140, 159, 165, 168, 172, 192, 195, 198, 213, 216, 218, 228, 237, 273, 295, 298, 303, 304, 309, 322, 327, 330, 338, 342, 356, 360, 366, 387, 393, 408, 416, 429, 432, 441, 447, 456
(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^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, a(n) such that a(n)^n = smallest interprime (of the form a^n) are in A075234.
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LINKS
| Zak Seidov, Table of n, a(n) for n=1..1317, a(n)<20000
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FORMULA
| a(n)=sqrt(A069495(n)) (Zak Seidov)
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EXAMPLE
| 3 is a member because 3^2 = 9 is the average of two successive primes 7 and 11.
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MAPLE
| s := 2: 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]; Select[ Range[464], 2#^2 == PrevPrim[ #^2] + NextPrim[ #^2] &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 14 2002)
n2ipQ[n_]:=Module[{n2=n^2}, (NextPrime[n2]+NextPrime[n2, -1])/2==n2]; Select[Range[500], n2ipQ] (* From Harvey P. Dale, May 04 2011 *)
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CROSSREFS
| Cf. A024675, A072568, A072569, A075190, A075191, A075192.
Cf. A075228, A075229, A075230, A075231, A075232, A075234.
Sequence in context: A047360 A004825 A028821 * A047243 A099148 A029787
Adjacent sequences: A075187 A075188 A075189 * A075191 A075192 A075193
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 09 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 14 2002
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