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A067836
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Let a(1)=2, f(n)=a(1)*a(2)*...*a(n-1) for n>=1 and a(n)=nextprime(f(n)+1)-f(n) for n>=2, where nextprime(x) is the smallest prime > x.
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4
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2, 3, 5, 7, 13, 11, 17, 19, 23, 37, 73, 29, 31, 43, 79, 53, 83, 67, 41, 47, 179, 149, 181, 103, 71, 59, 197, 167, 109, 137, 107, 251, 101, 157, 199, 283, 211, 277, 173, 127, 269, 61, 89, 271, 151, 191, 227, 311, 409, 577, 331, 281, 313, 307, 223, 491, 439, 233, 367
(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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LINKS
| Frank Buss, Prime Puzzles - Frank Buss's Conjecture
Frank Buss, The B(n) function
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MATHEMATICA
| <<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)
f[1]=1; 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 := 1:for n from 1 to 50 do a := nextprime(f+2)-f:f := f*a:print(a) end_for
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CROSSREFS
| Cf. A062894 has the indices of the primes in this sequence. A071290 has the sequence of f's. Also see A067362, A068192.
Sequence in context: A126056 A126055 A126054 * A108546 A065107 A185956
Adjacent sequences: A067833 A067834 A067835 * A067837 A067838 A067839
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KEYWORD
| nonn
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AUTHOR
| Frank Buss (fb(AT)frank-buss.de), Feb 09 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 02 2002 and by Dean Hickerson and David W. Wilson (davidwwilson(AT)comcast.net) Jun 10 2002
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