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A006512 Greater of twin primes.
(Formerly M3763)
462
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 (which is possible only if 2 is one of the primes). - Cino Hilliard, Jul 02 2004, edited by M. F. Hasler, Nov 14 2019
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
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
The phrase "x is an element of the {primes, positive integers} and there {exist no, exist} elements a,b of {1 and primes, primes}: a+b=x" determines A133410, A067829, A025584, A006512, A166081, A014092, A014091 and A038609 for the first few hundred terms with only de-duplication or omitting/including 3, 4 and 6 in the case of A166081/A014091 and one case of omitting/including 3 given 1 isn't prime. - Harry G. Coin, Nov 25 2015
The yet unproved Twin Prime Conjecture states that this sequence is infinite. - M. F. Hasler, Nov 14 2019
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
Harvey Dubner, Twin Prime Statistics, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.2.
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Wikipedia, Twin prime.
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 *)
Cases[Prime[Range[500]] + 2, _?PrimeQ] (* Fred Patrick Doty, Aug 23 2017 *)
PROG
(PARI) select(p->isprime(p-2), primes(1000))
(Magma) [n: n in PrimesUpTo(1610)|IsPrime(n-2)]; // Bruno Berselli, Feb 28 2011
(Haskell)
a006512 = (+ 2) . a001359 -- Reinhard Zumkeller, Feb 10 2015
(PARI) a(n)=p=3; while(p+2 < (p=nextprime(p+1)) || n-->0, ); p
vector(100, n, a(n)) \\ Altug Alkan, Dec 04 2015
(Python)
from sympy import primerange, isprime
print([n for n in primerange(1, 2001) if isprime(n - 2)]) # Indranil Ghosh, Jul 20 2017
CROSSREFS
Subsequence of A139690.
Bisection of A077800.
Sequence in context: A106986 A218011 A242255 * A074304 A264865 A293712
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified July 23 13:44 EDT 2024. Contains 374549 sequences. (Running on oeis4.)