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Numbers n for which there are at least as many primes in the range [prime(n)*prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)*prime(n+1)].
5

%I #12 Mar 31 2015 00:28:29

%S 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,27,28,29,

%T 30,31,32,33,34,35,36,37,40,46,47,51,52,53,54,56,57,60,62,64,66,67,68,

%U 70,71,72,75,76,78,79,80,82,83,84,85,87,89,90,91,93,94,95,97,99,100

%N Numbers n for which there are at least as many primes in the range [prime(n)*prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)*prime(n+1)].

%C Positions of nonnegative terms in A256470.

%H Antti Karttunen, <a href="/A256474/b256474.txt">Table of n, a(n) for n = 1..3457</a>

%t Select[Range@100, Count[Range[Prime[#] Prime[# + 1], Prime[# + 1]^2], _?PrimeQ] >= Count[Range[Prime[#]^2, Prime[#] Prime[# + 1]], _?PrimeQ] &] (* _Michael De Vlieger_, Mar 30 2015 *)

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A256474 (MATCHING-POS 1 1 (lambda (n) (<= 0 (A256470 n)))))

%Y Complement: A256475.

%Y Union of A256471 and A256476.

%Y Cf. A256484 (corresponding primes).

%Y Cf. A256470.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 30 2015