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 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 Pierre CAMI, Table of n, a(n) for n=2..2000 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 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 July 22 19:00 EDT 2024. Contains 374540 sequences. (Running on oeis4.)