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Search: id:A160434
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| A160434 |
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a(n) is the least number k such that (k-th prime after A002110(n)+1)-A002110(n) is not a prime |
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+0
1
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| 2, 3, 7, 11, 20, 26, 30, 37, 43, 44, 42, 64, 66, 46, 70, 87, 99, 91, 78, 95, 133, 119, 113, 133, 121, 132, 134, 151, 129, 204, 221, 164, 176, 162, 177, 169, 172, 207
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The conjecure on the fortunate numbers rephrased with a(n) is:
a(n)>=2 for all n>=0.
More generally, is a(n)>n+1 always true, or even a(n)>ln(n+1)*(n+1)?
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EXAMPLE
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a(3)=11: A002110(3)+1=2*3*5+1=31. The 11 primes after 31 are 37,41,43,47,53,59,61,67,71,73 and 79.
Subtracting 2*3*5=30 from each yields:
7,11,13,17,23,29,31,37,41,43,49.
These are primes except for the 11th value, which is 49=7^2.
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MAPLE
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a(n):=proc(n) option remember; local k: for k from 1 while isprime((nextprime@@k)(A002110(n)+1)-A002110(n)) do od:
k; end;
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CROSSREFS
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A002110, A005235, A160433, A002110
Adjacent sequences: A160431 A160432 A160433 this_sequence A160435 A160436 A160437
Sequence in context: A055502 A003173 A159262 this_sequence A139630 A133044 A014529
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KEYWORD
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hard,more,nonn,unkn
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AUTHOR
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Frederick Magata (frederick.magata(AT)web.de), May 13 2009
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