Search: id:A055211
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%I A055211
%S A055211 3,7,11,13,17,29,23,43,41,73,59,47,89,67,73,107,89,101,127,97,83,89,97,
%T A055211 251,131,113,151,263,251,223,179,389,281,151,197,173,239,233,191,223,
%U A055211 223,293,593,293,457,227,311,373,257,307,313,607,347,317,307,677,467
%N A055211 Lesser Fortunate numbers.
%C A055211 a(1) is not defined. The first 1000 terms are all prime and it is conjectured 
               that all terms are primes.
%C A055211 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
%H A055211 Pierre CAMI, <a href="b055211.txt">Table of n, a(n) for n=2..2000</a>
%H A055211 C. Banderier, <a href="http://algo.inria.fr/banderier/Computations/prime_factorial.html">
               Conjecture checked for n<1000</a> [It has been reported that this 
               data contains errors]
%F A055211 a(n) = 1 + the difference between the n-th Primorial less one and the 
               previous prime.
%e A055211 a(3) = 7 since 2*3*5 = 30, 30-1 = 29, previous prime is 23, 30-23 = 7.
%p A055211 for n from 2 to 60 do printf(`%d,`,product(ithprime(j), j=1..n) - prevprime(product(ithprime(j), 
               j=1..n)-1)) od:
%t A055211 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} ]
%t A055211 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}]
%Y A055211 Cf. A005235.
%Y A055211 Sequence in context: A089690 A020574 A020618 this_sequence A045417 A123988 
               A045418
%Y A055211 Adjacent sequences: A055208 A055209 A055210 this_sequence A055212 A055213 
               A055214
%K A055211 nonn
%O A055211 2,1
%A A055211 Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2000

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