cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A006512 Greater of twin primes.

Original entry on oeis.org

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
Offset: 1

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Author

N. J. A. Sloane

Keywords

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

Crossrefs

Subsequence of A139690.
Bisection of A077800.
Cf. A001097, A001359, A014574, A067829, A002476.

Programs

  • Haskell
    a006512 = (+ 2) . a001359 -- Reinhard Zumkeller, Feb 10 2015
  • Magma
    [n: n in PrimesUpTo(1610)|IsPrime(n-2)]; // Bruno Berselli, Feb 28 2011
  • 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 *)
  • PARI
    select(p->isprime(p-2),primes(1000))
  • 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

A175072 Natural numbers m with result 2 under iterations of {r mod (max prime p < r)} starting at r = m.

Original entry on oeis.org

2, 5, 7, 9, 13, 15, 19, 21, 25, 28, 31, 33, 36, 39, 43, 45, 49, 52, 55, 58, 61, 63, 66, 69, 73, 75, 78, 81, 85, 88, 91, 94, 96, 99, 103, 105, 109, 111, 115, 118, 120, 122, 126, 129, 133, 136, 139, 141, 144, 146, 148, 151
Offset: 1

Views

Author

Jaroslav Krizek, Jan 23 2010

Keywords

Comments

Complement of A175071.
Union of A175075 and A175076. [From Jaroslav Krizek, Jan 30 2010, A-numbers corrected R. J. Mathar, Feb 19 2010]

Examples

			Iteration procedure for a(6) = 15: 15 mod 13 = 2. Iteration procedure for a(10) = 28: 28 mod 23 = 5, 5 mod 3 = 2.

A175080 Primes q (except greater of twin primes) with result 2 under iterations of {r mod (max prime p < r)} starting at r = q.

Original entry on oeis.org

2, 2999, 3299, 5147, 5981, 8999, 9587, 10037, 10427, 10559, 10937, 11579, 12889, 13367, 14143, 14591, 14621, 15859, 16301, 16871, 18041, 18839, 18947, 19661, 21059, 21557, 22229, 22343, 22853, 23399, 23957, 24317, 24659, 25523, 27179
Offset: 1

Views

Author

Jaroslav Krizek, Jan 23 2010

Keywords

Comments

Subsequence of A175075. Union of a(n) and sequence A006512 (greater of twin primes) is A175075.

Examples

			Iteration procedure for a(2) = 2999: 2999 mod 2971 = 28, 28 mod 23 = 5, 5 mod 3 = 2.

Links

Programs

  • Mathematica
    mpQ[n_]:=!PrimeQ[n-2]&&MemberQ[NestWhileList[Mod[#,NextPrime[#,-1]]&,n,#>0&],2]; Select[Prime[Range[3000]],mpQ] (* Harvey P. Dale, Mar 10 2013 *)

A175076 Composites c which end at 2 under iterations of {r mod (max prime p < r)} starting at r = c.

Original entry on oeis.org

9, 15, 21, 25, 28, 33, 36, 39, 45, 49, 52, 55, 58, 63, 66, 69, 75, 78, 81, 85, 88, 91, 94, 96, 99, 105, 111, 115, 118, 120, 122, 126, 129, 133, 136, 141, 144, 146, 148, 153, 156, 159, 162, 165, 169, 172, 175, 178, 183, 186, 188, 190, 195, 201, 204, 206, 208, 213, 216
Offset: 1

Views

Author

Jaroslav Krizek, Jan 23 2010

Keywords

Comments

Subsequence of A175072. Union of a(n) and A175075 is A175072.

Examples

			Iteration procedure for a(2) = 15: 15 mod 13 = 2. Iteration procedure for a(5) = 28: 28 mod 23 = 5, 5 mod 3 = 2.

Programs

  • Mathematica
    ce2Q[n_]:=NestWhileList[Mod[#,NextPrime[#,-1]]&,n,#>0&][[-2]]==2; Select[ Range[ 300],CompositeQ[#]&&ce2Q[#]&] (* Harvey P. Dale, Feb 09 2015 *)

Extensions

More terms from R. J. Mathar, Sep 25 2010
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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