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A075058
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1 followed by the greatest primes selected to form a complete sequence (see algorithm below).
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3
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1, 2, 3, 7, 13, 23, 47, 97, 193, 383, 769, 1531, 3067, 6133, 12269, 24533, 49069, 98129, 196247, 392503, 785017, 1570007, 3140041, 6280067, 12560147, 25120289, 50240587, 100481167, 200962327, 401924639, 803849303, 1607698583, 3215397193, 6430794373
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This sequence starts at a(0)=1, subsequent terms a(n) for n>0 being obtained by selecting the (greatest prime) <= Sum(a(i),(i,0,n-1))+1. This ensures that the sequence is complete because Sum(a(i),(i,0,n-1))>=a(n)-1, for all n>=0 and a(0)=1, is a necessary and sufficient condition for completeness.
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LINKS
| Wikipedia, Complete sequence
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FORMULA
| a(n) = (greatest prime) <= Sum(a(i),(i,0,n-1))+1.
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EXAMPLE
| Given that the first 7 terms of the sequence are 1,2,..,23,47 then a(8)=(greatest prime)<=(1+2+..+23,47)+1=97, hence a(8)=97.
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MATHEMATICA
| prevprime[n_Integer] := (j=n; While[!PrimeQ[j], j--]; j) aprime[0]=1; aprime[n_Integer] := (aprime[n] = prevprime[Sum[aprime[m], {m, 0, n - 1}] + 1]); Table[aprime[p], {p, 0, 50}]
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CROSSREFS
| Cf. A068524, A007924, A066352, A200947.
Sequence in context: A088175 A091440 A175211 * A128695 A024504 A088172
Adjacent sequences: A075055 A075056 A075057 * A075059 A075060 A075061
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 07 2002
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EXTENSIONS
| Entry revised by Frank M Jackson (fjackson(AT)matrix-logic.co.uk), Dec 03 2011
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