

A055211


Lesser Fortunate numbers.


19



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
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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
Lim_{N>inf} (Sum_{n=2..N} a(n)) / (Sum_{n=2..N} prime(n)) = Pi/2; floor (a(n) / prime(n)) is always < 8.  Pierre CAMI, Aug 19 2017


LINKS

Pierre CAMI, Table of n, a(n) for n=2..2000
C. Banderier, Conjecture checked for n<1000 [It has been reported that this data contains errors]
Pierre CAMI, PFGW Script


FORMULA

a(n) = 1 + the difference between the nth Primorial less one and the previous prime.


EXAMPLE

a(3) = 7 since 2*3*5 = 30, 301 = 29, previous prime is 23, 3023 = 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++ ]; 2m1); Table[a[n], {n, 2, 60}]


CROSSREFS

Cf. A002110, A005235.
Sequence in context: A020574 A020618 A184865 * A183176 A045417 A260379
Adjacent sequences: A055208 A055209 A055210 * A055212 A055213 A055214


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Jul 04 2000


STATUS

approved



