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

2, 5, 11, 17, 19, 29, 41, 43, 59, 71, 79, 83, 101, 107, 109, 127, 137, 149, 163, 179, 191, 197, 227, 229, 239, 269, 281, 283, 311, 313, 331, 347, 349, 353, 379, 383, 397, 401, 419, 431, 439, 443, 461, 463, 487, 499, 503, 521, 541, 569, 571, 599, 617, 641, 643

Offset: 0

Author

Michel ten Voorde, Aug 02 2001

Keywords

• nonn
• easy

Comments

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

Examples

			a(2) = 5 because 7*7 < 5*11.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A122535, A147812.

Programs

Maple

N:= 1000: # to get all entries where prime(n+2) <= N
Primes:= select(isprime,[2,seq(2*i+1,i=1..floor((N-1)/2))]):
J:= select(j -> Primes[j+1]^2Robert Israel, Jun 23 2015

PARI

j=[]; for(n=1,400, if(prime(n+1)^2<(prime(n)*prime(n+2)),j=concat(j, prime(n)))); j

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

Extensions

More terms from Jason Earls, Aug 03 2001