

A002822


Numbers n such that 6n1, 6n+1 are twin primes.
(Formerly M0641 N0235)


56



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
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OFFSET

1,2


COMMENTS

6n1 and 6n+1 are twin primes iff n is not of the form 6ab+a+b.  Jon Perry, Feb 01 2002
The above equivalence was rediscovered by Balestrieri, see link. [Charles R Greathouse IV, Jul 05 2011]
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, Apr 03 2002
A002822 U A067611 U A171696 = A001477. [From JuriStepan Gerasimov, Feb 14 2010]


REFERENCES

S. W. Golomb, Problem E969, Amer. Math. Monthly, 58 (1951), 338; 59 (1952), 44.
W. J. LeVeque, Topics in Number Theory. AddisonWesley, 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).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
F. Balestrieri, An Equivalent Problem To The Twin Prime Conjecture, arXiv:1106.6050v1 [math.GM]


FORMULA

a(n) = A014574(n+1)/6.  Ivan N. Ianakiev, Aug 19 2013


MATHEMATICA

Select[ Range[350], PrimeQ[6#  1] && PrimeQ[6# + 1] & ]


PROG

(MAGMA) [n: n in [1..200]  IsPrime(6*n+1) and IsPrime(6*n1)] [From Vincenzo Librandi, Nov 21 2010]
(PARI) select(primes(100), n>isprime(n2)&&n>5)\6 \\ Charles R Greathouse IV, Jul 05 2011


CROSSREFS

Complement of A067611.
Equal to A014574(n)/6 for n>1.
Sequence in context: A062442 A036964 A067162 * A191327 A109598 A117959
Adjacent sequences: A002819 A002820 A002821 * A002823 A002824 A002825


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001


STATUS

approved



