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A006512 Greater of twin primes.
(Formerly M3763)
272
5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also primes that are the sum of two primes. - Cino Hilliard, Jul 02 2004

The set of greater of twin primes larger than five is a proper subset of the set of primes of the form 3n + 1 (A002476). - Paul Muljadi, Jun 05 2008

Smallest prime>n-th isolated composite. - Juri-Stepan Gerasimov, Nov 07 2009

Subsequence of A175075. Union of a(n) and sequence A175080 is A175075. - Jaroslav Krizek, Jan 30 2010

A164292(a(n))=1; A010051(a(n)+2)=0 for n>1. - Reinhard Zumkeller, Mar 29 2010

Omega(n)=Omega(n-2); d(n)=d(n-2). - Juri-Stepan Gerasimov, Sep 19 2010

Solutions of the equation (n-2)'+n'=2, where n' is the arithmetic derivative of n. - Paolo P. Lava, Dec 18 2012

Aside from the first term, all subsequent terms have digital root 1, 4, or 7. - J. W. Helkenberg, Jul 24 2013

Also primes p with property that the sum of the successive gaps between primes <= p is a prime number. - Robert G. Wilson v, Dec 19 2014

REFERENCES

See A001359 for further references and links.

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

Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Index entries for primes, gaps between

MAPLE

for i from 1 to 253 do if ithprime(i+1) = ithprime(i) + 2 then print({ithprime(i+1)}); fi; od; # Zerinvary Lajos, Mar 19 2007

P := select(isprime, [$1..1609]): select(p->member(p-2, P), P); # Peter Luschny, Mar 03 2011

A006512 := proc(n)

    2+A001359(n) ;

end proc: # R. J. Mathar, Nov 26 2014

MATHEMATICA

Select[ Prime[ Range[254]], PrimeQ[ # - 2] &] (* Robert G. Wilson v, Jun 09 2005 *)

Transpose[Select[Partition[Prime[Range[300]], 2, 1], Last[#]-First[#] == 2&]][[2]] (* Harvey P. Dale, Nov 02 2011 *)

PROG

(PARI) select(primes(1000), p->isprime(p-2)) \\ version 2.4.2 and before

select(p->isprime(p-2), primes(1000)) \\ newer versions

(MAGMA) [n: n in PrimesUpTo(1610)|IsPrime(n-2)];  // Bruno Berselli, Feb 28 2011

CROSSREFS

Cf. A001097, A001359, A014574, A067829, A002476.

Bisection of A077800.

Subsequence of A139690.

Sequence in context: A106986 A218011 A242255 * A074304 A072677 A117249

Adjacent sequences:  A006509 A006510 A006511 * A006513 A006514 A006515

KEYWORD

nonn,nice,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 21 10:09 EST 2014. Contains 252304 sequences.