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A356190 a(n) is the least prime p such that there are exactly n primes strictly between p and 2*p, or -1 if there is no such p. 1

%I #9 Aug 18 2022 11:44:32

%S 2,7,11,17,23,29,31,-1,37,-1,53,61,59,71,79,89,-1,109,97,101,-1,-1,

%T 127,-1,137,151,149,157,-1,179,-1,191,-1,-1,211,-1,-1,223,233,-1,251,

%U 257,263,293,-1,-1,-1,-1,307,311,-1,-1,-1,331,349,347,367,373,379,389,409,-1,-1,419,-1,431,443

%N a(n) is the least prime p such that there are exactly n primes strictly between p and 2*p, or -1 if there is no such p.

%H Robert Israel, <a href="/A356190/b356190.txt">Table of n, a(n) for n = 1..9999</a>

%F a(n) <= A168421(n+1) - 2, with equality for n = 6, 263, 3061, 4750, 4893, 5029, 5555, 6101, ....

%e a(3) = 11 because there are exactly 3 primes between 11 and 22, namely 13, 17 and 19, and 11 is the least prime that works.

%p V:= Vector(100,-1): p:= 1:

%p for n from 1 while p < 727 do # note that A168421(101) = 727

%p p:= nextprime(p);

%p v:= numtheory:-pi(2*p)-n;

%p if v <= 100 and V[v] = -1 then

%p V[v]:= p;

%p fi

%p od:

%p convert(V,list);

%Y Cf. A168421.

%K sign

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jul 29 2022

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