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Search: id:A002822
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| A002822 |
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Numbers n such that 6n-1, 6n+1 are twin primes.
(Formerly M0641 N0235)
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+0
43
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| 1, 2, 3, 5, 7, 10, 12, 17, 18, 23, 25, 30, 32, 33, 38, 40, 45, 47, 52, 58, 70, 72, 77, 87, 95, 100, 103, 107, 110, 135, 137, 138, 143, 147, 170, 172, 175, 177, 182, 192, 205, 213, 215, 217, 220, 238, 242, 247, 248, 268, 270, 278, 283, 287, 298, 312, 313, 322, 325
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Iff n is not of the form 6ab+-a+-b, then 6n-1 and 6n+1 are twin primes. - Jon Perry (perry(AT)globalnet.co.uk), Feb 01 2002
Even entries correspond to twin primes of the form (4k - 1,4k + 1), odd entries to twin primes of the form (4k + 1,4k + 3). - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 03 2002
A002822 U A067611 U A171696 = A001477. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Feb 14 2010]
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REFERENCES
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S. W. Golomb, Problem E969, Amer. Math. Monthly, 58 (1951), 338; 59 (1952), 44.
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 1, p. 69.
W. Sierpi\'{n}ski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 120.
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
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T. D. Noe, Table of n, a(n) for n = 1..10000
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MAPLE
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ZL:=[]:for p from 5 to 1950 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL), (((p+2)^2)-p^2)/24]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2007
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MATHEMATICA
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Select[ Range[350], PrimeQ[6# - 1] && PrimeQ[6# + 1] & ]
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CROSSREFS
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Complement of A067611.
Equal to A014574(n)/6 for n>0.
Sequence in context: A062442 A036964 A067162 this_sequence A109598 A117959 A117952
Adjacent sequences: A002819 A002820 A002821 this_sequence A002823 A002824 A002825
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KEYWORD
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nonn,nice,easy,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001
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