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Search: id:A113339
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| A113339 |
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Integers n such that prime(n+1)-prime(n) is nonprime, square-free. Except for the initial term of 1, the terms are k-semiprime for some k>=2. |
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+0
2
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| 1, 9, 11, 15, 16, 18, 21, 23, 30, 32, 34, 36, 37, 39, 40, 42, 51, 53, 54, 55, 56, 58, 61, 62, 66, 67, 68, 71, 73, 74, 76, 80, 82, 84, 86, 96, 100, 101, 102, 103, 105, 106, 107, 108, 110, 111, 115, 118, 119, 123, 125, 127, 129, 130, 133, 137, 138, 141, 145, 146, 150
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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prime(n+1)-prime(n)=1 or p1*...*pk where p1, ..., pk are two or more distinct primes.
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EXAMPLE
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prime(69)-prime(68)=347-337=10=2*5.
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MAPLE
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L:=[]: for z to 1 do for k from 1 to 200 do p:=ithprime(k); q:=nextprime(p); x:=q-p; if not(isprime(x)) and issqrfree(x) then L:=[op(L), k] fi od od; L;
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CROSSREFS
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Cf. A000040, A000469, A001358.
Sequence in context: A027726 A044873 A101754 this_sequence A037009 A163096 A027694
Adjacent sequences: A113336 A113337 A113338 this_sequence A113340 A113341 A113342
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KEYWORD
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easy,nonn
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AUTHOR
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Walter A. Kehowski (wkehowski(AT)cox.net), Jan 08 2006
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