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!)
A055211 Lesser Fortunate numbers. 18
3, 7, 11, 13, 17, 29, 23, 43, 41, 73, 59, 47, 89, 67, 73, 107, 89, 101, 127, 97, 83, 89, 97, 251, 131, 113, 151, 263, 251, 223, 179, 389, 281, 151, 197, 173, 239, 233, 191, 223, 223, 293, 593, 293, 457, 227, 311, 373, 257, 307, 313, 607, 347, 317, 307, 677, 467 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
a(1) is not defined. The first 1000 terms are all prime and it is conjectured that all terms are primes.
a(n) is the smallest m such that m > 1 and A002110(n) - m is prime. For n > 2, a(n) must be greater than prime(n+1) - 1. - Farideh Firoozbakht, Aug 20 2003
LINKS
Cyril Banderier, Conjecture checked for n<1000 [It has been reported that this data contains errors]
Pierre CAMI, PFGW Script
Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.
FORMULA
a(n) = 1 + the difference between the n-th primorial less one and the previous prime.
From Pierre CAMI, Aug 19 2017: (Start)
Limit_{N->oo} (Sum_{n=2..N} a(n)) / (Sum_{n=2..N} prime(n)) = Pi/2.
Floor(a(n) / prime(n)) is always < 8. (End)
Conjecture: Limit_{N->oo} (Sum_{n=2..N} a(n)) / (Sum_{n=2..N} prime(n)) = 3/2. - Alain Rocchelli, Nov 07 2022
EXAMPLE
a(3) = 7 since 2*3*5 = 30, 30-1 = 29, previous prime is 23, 30-23 = 7.
MAPLE
for n from 2 to 60 do printf(`%d, `, product(ithprime(j), j=1..n) - prevprime(product(ithprime(j), j=1..n)-1)) od:
MATHEMATICA
PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; k ]; Primorial[ n_Integer ] := Module[ {k = Product[ Prime[ j ], {j, 1, n} ]}, k ]; LF[ n_Integer ] := (p = Primorial[ n ] - 1; q = PrevPrime[ p ]; p - q + 1); Table[ LF[ n ], {n, 2, 60} ]
a[2]=3; a[n_] := (For[m=(Prime[n+1]+1)/2, !PrimeQ[Product[Prime[k], {k, n}] - 2m+1], m++ ]; 2m-1); Table[a[n], {n, 2, 60}]
CROSSREFS
Sequence in context: A020574 A020618 A184865 * A183176 A045417 A260379
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 04 2000
STATUS
approved

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 July 22 19:00 EDT 2024. Contains 374540 sequences. (Running on oeis4.)