

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
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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



