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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
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
Sequence in context: A188836 A030146 A229970 * A158146 A158147 A158148
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

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Last modified March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)