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Search: id:A100380
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| A100380 |
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Least k such that p(n)+p(k)# is prime, where p(i)=i-th prime, p(i)#=i-th primorial. |
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+0
1
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| 1, 1, 2, 1, 2, 1, 4, 2, 1, 2, 2, 1, 3, 2, 2, 1, 2, 2, 1, 2, 3, 2, 5, 2, 1, 2, 1, 3, 5, 3, 2, 1, 4, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 1, 3, 3, 2, 1, 4, 2, 1, 3, 2, 2, 2, 1, 2, 2, 1, 3, 4, 2, 1, 4, 3, 2, 3, 1, 3, 2, 3, 2, 2, 3, 2, 3, 4, 3, 3, 1, 4, 1, 2, 5, 2, 3, 2, 1, 4, 4, 3, 5, 3, 4, 2, 4, 1, 4, 2
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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Conjecture: all prime number can be written as + or - p(n) - or + p(k)#.
The sequence grows remarkably slowly. The largest number occurring within the first 50000 elements is 90. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006
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EXAMPLE
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p(8)=19
19+2=21 =3*7
19+6=25 =5*5
19+30=49 =7*7
19+210=229 prime 210=p(4)# so k(8)=4
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MATHEMATICA
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Table[k := 1; While[Not[PrimeQ[Prime[n]+Product[Prime[i], {i, 1, k}]]], k++ ]; k, {n, 2, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006
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CROSSREFS
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Sequence in context: A024559 A061797 A068341 this_sequence A080825 A034693 A072342
Adjacent sequences: A100377 A100378 A100379 this_sequence A100381 A100382 A100383
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KEYWORD
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easy,nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Dec 30 2004
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006
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