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A001632
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Smallest prime p such that there is a gap of 2n between p and previous prime.
(Formerly M3812 N1560)
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10
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5, 11, 29, 97, 149, 211, 127, 1847, 541, 907, 1151, 1693, 2503, 2999, 4327, 5623, 1361, 9587, 30631, 19373, 16183, 15727, 81509, 28277, 31957, 19661, 35671, 82129, 44351, 43391, 34123, 89753, 162209, 134581, 173429, 31469, 404671, 212777
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A001632(n) = 2n+A000230(n) = nextprime(A000230(n)).
Smallest prime preceded by 2n-1 successive composites. [From Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 23 2010]
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 97, p. 34, Ellipses, Paris 2008.
L. J. Lander and T. R. Parkin, On the first appearance of prime differences, Math. Comp., 21 (1967), 483-488.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..595 (from Nicely)
T. R. Nicely, List of prime gaps
Index entries for primes, gaps between
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EXAMPLE
| The first time a gap of 4 occurs between primes is between 7 and 11, so A000230(2)=7 and A001632(2)=11.
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PROG
| (PARI) default(primelimit, 10^7); a=[]; o=2; g=0; forprime(p=3, default(primelimit), bittest(g, (-o+o=p)\2) & next; a=concat(a, [[p, (p-precprime(p-1))/2]]); g+=1<<((p-precprime(p-1))\2)); a=vecsort(a, 2); for(i=2, #a, a[i][2]<i & print1(a[i][1]", ")) /* first element is [3, 1/2], cf. A000230(0). Limit 10^7 yields a(1), ..., a(70) in 0.5 sec @ 3GHz. */ - M. F. Hasler, Jan 13 2011
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CROSSREFS
| Cf. A000230, A002386.
Sequence in context: A084817 A183382 A100965 * A053185 A090119 A174922
Adjacent sequences: A001629 A001630 A001631 * A001633 A001634 A001635
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000 and from Labos, E., Nov 29, 2000.
Terms a(1)-a(38) checked with the PARI program by M. F. Hasler, Jan 13 2011.
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