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 A075192 Numbers k such that k^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 Amiram Eldar, Table of n, a(n) for n = 1..10000 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, A075191. Cf. A075228, A075229, A075230, A075231, A075232, A075233, 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 31 23:46 EDT 2021. Contains 346377 sequences. (Running on oeis4.)