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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 (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

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 n-th Primorial less one and the previous prime.

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

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

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)