login
This site is supported by donations 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
4, 9, 25, 49, 121, 221, 289, 529, 667, 899, 1147, 1591, 2021, 1849, 2773, 3551, 4087, 4819, 4757, 5041, 7519, 7663, 8549, 9991, 10379, 13231, 11227, 14659, 11881, 21877, 25283, 18209, 22331, 20989, 22499, 25591, 27221, 29503, 31313, 34547 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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.

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

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

LINKS

Dmitry Kamenetsky, Table of n, a(n) for n = 0..133

PROG

(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

CROSSREFS

Cf. A002110, A054757, A054758, A005235.

Sequence in context: A188836 A030146 A229970 * A158146 A158147 A158148

Adjacent sequences:  A038768 A038769 A038770 * A038772 A038773 A038774

KEYWORD

nonn

AUTHOR

Labos Elemer, May 04 2000

EXTENSIONS

Name edited by Tom Edgar, Jun 08 2015

a(0) prepended by Dmitry Kamenetsky, Jan 06 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 14 12:43 EDT 2019. Contains 328006 sequences. (Running on oeis4.)