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Search: id:A061092
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| A061092 |
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a(0) = 1; for n>0, a(n) = smallest prime of the form k*a(n-1) + 1. |
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+0
13
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| 1, 2, 3, 7, 29, 59, 709, 2837, 22697, 590123, 1180247, 9441977, 169955587, 2719289393, 5438578787, 32631472723, 391577672677, 1566310690709, 50121942102689, 1503658263080671, 9021949578484027, 360877983139361081
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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It has been established in the reference that for every prime p there exists at least one prime of the form k*p + 1. Hence the sequence is infinite.
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REFERENCES
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Amarnath Murthy, On the divisors of Smarandache Unary Sequence. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
M. L. Perez et al., eds., Smarandache Notions Journal
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EXAMPLE
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59 = 2*29 + 1; 709 = 12*59 + 1.
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MATHEMATICA
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a[1] = 2; a[n_] := a[n] = Block[{k = 1, p = a[n - 1]}, While[ !PrimeQ[k*p + 1], k++ ]; k*p + 1]; Table[ a[n], {n, 21}] (from Robert G. Wilson v Nov 26 2004)
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CROSSREFS
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Corresponding values of k are in A121799.
Sequence in context: A060412 A062573 A019435 this_sequence A084435 A072469 A004062
Adjacent sequences: A061089 A061090 A061091 this_sequence A061093 A061094 A061095
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KEYWORD
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nonn,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 19 2001
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EXTENSIONS
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More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), May 29 2001
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