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Search: id:A136437
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| A136437 |
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a(n)= p(n)- k! ; p(n) is n-th prime number; k is greatest number for which k!<=p(n). |
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5
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| 0, 1, 3, 1, 5, 7, 11, 13, 17, 5, 7, 13, 17, 19, 23, 29, 35, 37, 43, 47, 49, 55, 59, 65, 73, 77, 79, 83, 85, 89, 7, 11, 17, 19, 29, 31, 37, 43, 47, 53, 59, 61, 71, 73, 77, 79
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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How many times does each p(n) appears in this sequence ?
The only value (p(n)-k!)=0 is n=1;k=2.
Are n=2;k=2 and n=4;k=3 the only values (p(n)-k!)=1?
There exists infinitely many solutions in the form (p(n)-k!)=p(n-t), t<n.
Are there infinitely many solutions in the form
(p(n)-k!)= p(r_1)*...*p(r_i); r_i < n for all i ?
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FORMULA
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a(n)= p(n)- k! ; p(n) is n-th prime number; k is greatest number for which k!<=p(n)
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EXAMPLE
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a(1)= p(1)-2! = 2-2 = 0
a(2)= p(2)-2! = 3-2 = 1
a(3)= p(3)-2! = 5-2 = 3
a(4)= p(4)-3! = 7-6 = 1
a(5)= p(5)-3! = 11-6 = 5
a(6)= p(6)-3! = 13-6 = 7
a(7)= p(7)-3! = 17-6 = 11
a(8)= p(8)-3! = 19-6 = 13
a(9)= p(9)-3! = 23-6 = 17
a(10)= p(10)-4! = 29-24 = 5
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CROSSREFS
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Cf. A135996, A000040, A000142.
Sequence in context: A159285 A021080 A049764 this_sequence A137328 A140991 A038738
Adjacent sequences: A136434 A136435 A136436 this_sequence A136438 A136439 A136440
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 02 2008
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