login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038771 a(n) is the smallest composite number c such that A002110(n) + c is prime. 2

%I #44 Jan 07 2019 03:50:15

%S 4,9,25,49,121,221,289,529,667,899,1147,1591,2021,1849,2773,3551,4087,

%T 4819,4757,5041,7519,7663,8549,9991,10379,13231,11227,14659,11881,

%U 21877,25283,18209,22331,20989,22499,25591,27221,29503,31313,34547

%N a(n) is the smallest composite number c such that A002110(n) + c is prime.

%C The lower "envelope" of the sequence is prime(n+1)^2. See also Fortune-conjecture (A005235).

%C For some n, c=prime(n+1)^2; for others, it is larger, even not necessarily divisible by prime(n+1). E.g., at n=11, prime(11)=31 and a(11) = 1591 = 37*43 = prime(12)*prime(14), while for n=59, a(59) = 97969 = 313^2 = prime(65)^2, etc. Adding these to the suitable primorial numbers, primes are obtained.

%C Conjecture: lim inf_{n->oo} a(n)/prime(n+1)^2 = 1 < lim sup_{n->oo} a(n)/prime(n+1)^2 = 2. - _Charles R Greathouse IV_ and _Thomas Ordowski_, Apr 24 2015

%C Conjecture: all the terms in this sequence have exactly two prime factors. This conjecture is true for the first 133 terms. - _Dmitry Kamenetsky_, Jan 06 2019

%H Dmitry Kamenetsky, <a href="/A038771/b038771.txt">Table of n, a(n) for n = 0..133</a>

%o (PARI) a(n) = {my(q = prod(i=1, n, prime(i))); forcomposite(c = 1,, if (isprime(q+c), return(c);););} \\ _Michel Marcus_, May 24 2015

%Y Cf. A002110, A054757, A054758, A005235.

%K nonn

%O 0,1

%A _Labos Elemer_, May 04 2000

%E Name edited by _Tom Edgar_, Jun 08 2015

%E a(0) prepended by _Dmitry Kamenetsky_, Jan 06 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)