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.

A069457 Lowest primes in twin packs.

Original entry on oeis.org

3, 101, 137, 179, 419, 809, 1019, 1049, 1481, 1871, 1931, 2081, 2111, 2969, 3251, 3359, 3461, 4217, 4259, 5009, 5651, 5867, 6689, 6761, 6947, 7331, 7547, 8219, 8969, 9419, 10007, 11057, 11159, 11699, 12239, 13001, 13709, 13997
Offset: 1

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Author

Neil Fernandez, Mar 23 2002

Keywords

Comments

As the example (below) explains, "A twin pack of primes contains 2 or more pairs of twin primes, between which pairs there are no other primes." The key phrase is "or more." The first twin pack is therefore ((3,5),(5,7),(11,13),(17,19)). Because all of the consecutive primes from 3 to 19 are included in this twin pack, the lowest primes in the two pairs of twin primes ((5,7),(11,13)) and ((11,13),(17,19)) are not included because they are already subsumed in the first twin pack. - Harvey P. Dale, Mar 02 2025

Examples

			A twin pack of primes contains 2 or more pairs of twin primes, between which pairs there are no other primes. 137 is in the sequence because 137,139 are primes and the next primes are 149,151.
		

Crossrefs

Programs

  • Maple
    state:= 0: p:=13: Res:= 3: count:= 1;
    while count < 100 do
      q:= nextprime(p);
      if state = 0 then
         if q = p+2 then state:= 1; r:= p; p:= nextprime(q);
         else p:= q
         fi;
       elif state = 1 then
         if q = p+2 then
           count:= count+1; Res:= Res, r; state:= 2; p:= nextprime(q);
         else p:= q; state:= 0
         fi
       else
         if q = p+2 then
           p:= nextprime(q);
         else p:= q; state:= 0
         fi
       fi
    od:
    Res; # Robert Israel, Jan 13 2020