A069457 Lowest primes in twin packs.

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

1,1

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

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

Crossrefs

Cf. A001359, A048614, A053778.

Sequence in context: A128296 A037114 A336437 * A142416 A110625 A108220

Adjacent sequences: A069454 A069455 A069456 * A069458 A069459 A069460

Keyword

nonn,changed

Author

Neil Fernandez, Mar 23 2002

Status

approved