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A075192 Numbers n such that n^4 is an interprime = average of two successive primes. 10
3, 5, 8, 21, 55, 66, 87, 99, 104, 105, 110, 120, 129, 135, 141, 144, 152, 168, 172, 186, 187, 192, 211, 222, 243, 279, 283, 295, 297, 321, 342, 385, 395, 398, 408, 425, 426, 460, 520, 541, 559, 597, 626, 627, 638, 642, 657, 666, 673, 680, 713, 755, 759, 765 (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^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.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

3 belongs to this sequence because 3^4 = 81 is the average of two successive primes 79 and 83.

MAPLE

s := 4: for n from 2 to 1000 do if prevprime(n^s)+nextprime(n^s)=2*n^s then print(n) else; fi; od;

MATHEMATICA

intprQ[n_]:=Module[{c=n^4}, c==Mean[{NextPrime[c], NextPrime[c, -1]}]]; Select[Range[800], intprQ] (* Harvey P. Dale, Dec 01 2013 *)

CROSSREFS

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

Sequence in context: A112656 A002366 A141615 * A101984 A292492 A108460

Adjacent sequences:  A075189 A075190 A075191 * A075193 A075194 A075195

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 09 2002

EXTENSIONS

Edited by Robert G. Wilson v Sep 14 2002

STATUS

approved

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Last modified July 23 20:32 EDT 2019. Contains 325264 sequences. (Running on oeis4.)