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Search: id:A038771
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| A038771 |
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Smallest composite numbers such that Q+c is prime, where Q=A002110. |
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+0
1
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| 9, 25, 49, 121, 221, 289, 529, 667, 899, 1147, 1591, 2021, 1849, 2773, 3551, 4087, 4819, 4757, 5041, 7519, 7663, 8549, 9991, 10379, 13231, 11227, 14659, 11881, 21877, 25283, 18209, 22331, 20989, 22499, 25591, 27221, 29503, 31313, 34547
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The lower "envelope" of the sequence is p(n+1)^2. See also Fortune-conjecture (A005235).
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EXAMPLE
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For some n, c=Prime[n+1]^2, for others it is larger, even not necessarily divisible by Prime[n+1]. E.g. at n=11,p(11)=31 and a(11)=1591=37*43=p(12)*p(14), while for n=59, a(59)=97969=313^2=p(65)^2, etc... Adding these to the suitable primorial numbers, primes are obtained.
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CROSSREFS
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A002110, A054757, A054758, A005235.
Sequence in context: A110284 A109367 A110588 this_sequence A045972 A112629 A031162
Adjacent sequences: A038768 A038769 A038770 this_sequence A038772 A038773 A038774
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 04 2000
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