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A055211
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Lesser Fortunate numbers.
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16
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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; internal format)
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OFFSET
| 2,1
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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 (f.firoozbakht(AT)sci.ui.ac.ir), Aug 20 2003
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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]
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FORMULA
| a(n) = 1 + the difference between the n-th Primorial less one and the previous prime.
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EXAMPLE
| a(3) = 7 since 2*3*5 = 30, 30-1 = 29, previous prime is 23, 30-23 = 7.
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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:
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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}]
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CROSSREFS
| Cf. A005235.
Sequence in context: A020574 A020618 A184865 * A183176 A045417 A045418
Adjacent sequences: A055208 A055209 A055210 * A055212 A055213 A055214
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2000
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