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Search: id:A090975
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| A090975 |
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Least integer k such that n!+1-k is prime. |
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+0
1
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| 0, 0, 0, 0, 2, 8, 2, 2, 32, 14, 12, 0, 2, 24, 2, 48, 54, 60, 42, 102, 32, 32, 74, 90, 74, 150, 38, 0, 102, 32, 2, 62, 2, 2, 194, 114, 128, 0, 2, 74, 84, 0, 80, 110, 110, 54, 90, 80, 104, 60, 98, 180, 68, 60, 128, 62, 462, 278, 110, 138, 140, 72, 72, 102, 360, 128, 318, 192
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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The (n-1) consecutive numbers n!+2,...,n!+n (for n>=2) are not prime. This fact implies that there are arbitrarily large gaps in the distribution of the prime numbers. n!+1 itself may be a prime number as in the case of n=3, 11, 27 (see A002981 for all such n). Now a(n) measures, when the first prime number previous to n!+2 appears. Thus a(n)=8 means that n!+1-3 is prime, and so on. Obviously, the values of a(n) are always even numbers. Conjectures: |a(n)-1| is either 1 or a prime number. Is the growth of b(n) := sum(a(k),k=0..n) quadratic, that is b(n)=O(n^2)?
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EXAMPLE
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a(3)=0 because 3!+1-0=7 is prime.
a(4)=2 because 4!+1-2=23 is prime and 24 and 25 are not.
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MAPLE
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a := proc(n) option remember; n!+1-prevprime(n!+2); end;
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CROSSREFS
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Cf. A090786, A002981, A005095.
Adjacent sequences: A090972 A090973 A090974 this_sequence A090976 A090977 A090978
Sequence in context: A087198 A065813 A076344 this_sequence A083489 A074962 A064863
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KEYWORD
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nonn
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AUTHOR
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Frederick Magata (fmagata(AT)mi.uni-koeln.de), Feb 28 2004
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