A076957 - OEIS

%I #31 Aug 01 2021 19:14:28

%S 1,4,6,10,15,16,25,24,31,39,38,45,64,48,52,57,75,82,81,70,76,79,106,

%T 112,145,111,121,117,123,134,144,139,146,154,163,192,169,176,179,193,

%U 202,218,204,226,223,240,233,238,243,259,291,256,286,309,278

%N Smallest k such that there are exactly n primes strictly between k^2 and (k+1)^2.

%C From _David W. Wilson_, Jan 08 2017: (Start)

%C a(n)^2 = A076956(n).

%C A014085(a(n)) = n.

%C Conjecturally, a(n) is undefined for n = 1 and defined for all n >= 2. (End)

%H T. D. Noe and David W. Wilson, <a href="/A076957/b076957.txt">Table of n, a(n) for n = 2..10000</a> (a(n) for n = 2..1000 from T. D. Noe).

%p a := proc(n) local k, h, SEARCHLIMIT; SEARCHLIMIT := 10000; h := proc(k) option remember; nops(select(j->isprime(j), [$k^2+1..(k+1)^2])) end: k := 1; while h(k) <> n and k < SEARCHLIMIT do k := k+1 od; `if`(k=SEARCHLIMIT, print("Search limit reached!"), k) end: seq(a(n), n=2..56); # _Peter Luschny_, Jan 10 2017

%t Table[k = 1; While[Count[Map[PrimeQ, Range[k^2 + 1, (k + 1)^2]], True] != n, k++]; k, {n, 2, 56}] (* _Michael De Vlieger_, Jan 10 2017 *)

%t With[{pp=Table[Count[Range[n^2+1,(n+1)^2-1],_?(PrimeQ[#]&)],{n,500}]},Table[ Position[pp,k,1,1],{k,60}]]//Flatten (* _Harvey P. Dale_, Aug 01 2021 *)

%Y Cf. A014085, A076956, A084597.

%K nonn

%O 2,2

%A _Amarnath Murthy_, Oct 20 2002

%E More terms from _Ralf Stephan_, Oct 31 2002