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A049591
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Odd primes p such that p+2 is composite.
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8
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7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 349, 353, 359, 367, 373, 379, 383, 389
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes p such that nextprime(p)-p >= 4.
Primes p such that p+2 divides (p-1)!.
Odd primes n such that n!*B(n+1) is an integer, where B(k) are the Bernoulli numbers. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 06 2002
Sequence appears also to give all n>1 such that there is no prime p satisfying the inequality n<p<n+tau(n)^2 where tau(n)=A000005(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2002
Conjecture: start from any initial value f(1)>=2 and define f(n) to be the largest prime factor of f(1)+f(2)+...+f(n-1) then f(n)=n/2+O(log(n)) and there are infinitely primes p such that f(2p)=p. Conjecture: current sequence gives primes satisfying f(2p)=p when f(1)=3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2003
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REFERENCES
| K. Soundararajan, Small gaps bewteen prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18.
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LINKS
| Index entries for primes, gaps between
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EXAMPLE
| 13 is here because it is prime and 15 is composite. Also 15 divides 12!.
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MAPLE
| d:=4; M:=1000; t0:=[]; for n from 1 to M do p:=ithprime(n); if nextprime(p) - p >= d then t0:=[op(t0), p]; fi; od: t0;
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CROSSREFS
| Cf. A067774.
Cf. A105399.
Sequence in context: A088982 A176406 A033561 * A176180 A058620 A038910
Adjacent sequences: A049588 A049589 A049590 * A049592 A049593 A049594
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2003
Edited by Don Reble (djr(AT)nk.ca), Dec 20 2006
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