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A134204
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a(0)=2; for n>0, a(n) = smallest prime not occurring earlier in the sequence such that a(n-1)+a(n) is a multiple of n.
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10
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2, 3, 5, 7, 13, 17, 19, 23, 41, 31, 29, 37, 11, 67, 59, 61, 83, 53, 73, 79, 101, 109, 89, 233, 103, 47, 239, 139, 113, 293, 97, 151, 137, 127, 43, 167, 157, 509, 251, 373, 107, 467, 163, 181, 347, 193, 313, 439, 281, 307, 443, 271, 197, 227, 367, 733, 331, 353, 401, 71, 229
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Is this sequence infinite and, if so, is it a permutation of the primes?
This sequence is infinite if and only if a(n-1) never divides n for any n.
This sequence exists for at least 800*10^6 terms. - David Applegate, Nov 01 2007, Nov 15 2007
The plot of primes less than 10^6 shows an interesting crosshatch pattern. Why? [From T. D. Noe (noe(AT)sspectra.com), Jul 12 2009]
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LINKS
| Robert Israel, Table of n, a(n) for n = 0..1000
T. D. Noe, Plot of primes less than 10^6 [From T. D. Noe (noe(AT)sspectra.com), Jul 12 2009]
N. J. A. Sloane, Eight Hateful Sequences, a short paper for the 8th Gathering for Gardner, May 2008. [From T. D. Noe (noe(AT)sspectra.com), Jul 12 2009]
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EXAMPLE
| The primes that don't occur among terms a(0) through a(6) form the sequence 11,23,29,31,... Of these, 23 is the smallest that when added to a(6)=19 gets a multiple of 7 -- 19+23 = 42 = 6*7. (19+11 = 30, which is not a multiple of 7.) So a(7) = 23.
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CROSSREFS
| Cf. A134205, A134206, A134207, A133242, A133243, A131261.
For records see A133244, A133245.
A162846 (where prime(n) occurs) [From T. D. Noe (noe(AT)sspectra.com), Jul 19 2009]
Sequence in context: A052015 A042992 A049567 * A134207 A133244 A077040
Adjacent sequences: A134201 A134202 A134203 * A134205 A134206 A134207
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KEYWORD
| nonn,nice
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AUTHOR
| Leroy Quet Oct 14 2007
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EXTENSIONS
| More terms from Robert Israel, Oct 14 2007
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