cp's OEIS Frontend

A063535 Primes prime(n) such that prime(n+1)^2 < prime(n)*prime(n+2).

%I A063535 #28 Apr 21 2021 04:40:23
%S A063535 2,5,11,17,19,29,41,43,59,71,79,83,101,107,109,127,137,149,163,179,
%T A063535 191,197,227,229,239,269,281,283,311,313,331,347,349,353,379,383,397,
%U A063535 401,419,431,439,443,461,463,487,499,503,521,541,569,571,599,617,641,643
%N A063535 Primes prime(n) such that prime(n+1)^2 < prime(n)*prime(n+2).
%C A063535 Conjecture:  these are the primes such that prime(n+2) - 2*prime(n+1) + prime(n) > 0.  If so, this sequence with A122535 and A147812 partition the primes. - _Clark Kimberling_, May 16 2015
%H A063535 Harry J. Smith, <a href="/A063535/b063535.txt">Table of n, a(n) for n = 0..1000</a>
%e A063535 a(2) = 5 because 7*7 < 5*11.
%p A063535 N:= 1000: # to get all entries where prime(n+2) <= N
%p A063535 Primes:= select(isprime,[2,seq(2*i+1,i=1..floor((N-1)/2))]):
%p A063535 J:= select(j -> Primes[j+1]^2<Primes[j]*Primes[j+2],[$1..nops(Primes)-2]):
%p A063535 Primes[J]; # _Robert Israel_, Jun 23 2015
%o A063535 (PARI) j=[]; for(n=1,400, if(prime(n+1)^2<(prime(n)*prime(n+2)),j=concat(j, prime(n)))); j
%o A063535 (PARI) { n=-1; for (m=1, 10^9, if (prime(m + 1)^2 < prime(m)*prime(m + 2), write("b063535.txt", n++, " ", prime(m)); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 25 2009
%Y A063535 Cf. A122535, A147812.
%K A063535 nonn,easy
%O A063535 0,1
%A A063535 _Michel ten Voorde_, Aug 02 2001
%E A063535 More terms from _Jason Earls_, Aug 03 2001