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A068192
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Let a(1)=2, f(n)=4*a(1)*a(2)*...*a(n-1) for n>=1 and a(n)=f(n)-prevprime(f(n)-1) for n>=2, where prevprime(x) is the largest prime <x.
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3
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2, 3, 5, 7, 11, 13, 17, 19, 31, 29, 23, 41, 43, 37, 89, 59, 53, 67, 79, 71, 137, 109, 239, 167, 199, 47, 83, 97, 61, 373, 101, 179, 193, 131, 151, 73, 263, 593, 139, 113, 157, 103, 241, 181, 397, 233, 617, 311, 191, 229, 271, 269, 127, 223, 331, 337, 211, 163
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?
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MATHEMATICA
| <<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)
f[1]=4; f[n_] := f[n]=f[n-1]a[n-1]; a[n_] := a[n]=Module[{i}, For[i=2, True, i++, If[ProvablePrimeQ[f[n]-i], Return[i]]]]
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PROG
| (MuPAD) f := 4:for n from 1 to 50 do a := f-numlib::prevprime(f-2):f := f*a:print(a) end_for
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CROSSREFS
| Cf. A068193 has the indices of the primes in this sequence. A066631 has the sequence of f's. Also see A067836.
Sequence in context: A079150 A177000 A117843 * A002200 A181561 A069709
Adjacent sequences: A068189 A068190 A068191 * A068193 A068194 A068195
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KEYWORD
| nonn
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AUTHOR
| Frank Buss (fb(AT)frank-buss.de), Feb 19 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 10 2002
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