A089628 Smallest member of a pair of consecutive twin prime pairs that have no primes between them.

3, 5, 11, 101, 137, 179, 191, 419, 809, 821, 1019, 1049, 1481, 1871, 1931, 2081, 2111, 2969, 3251, 3359, 3371, 3461, 4217, 4229, 4259, 5009, 5651, 5867, 6689, 6761, 6779, 6947, 7331, 7547, 8219, 8969, 9419, 9431, 9437, 10007, 11057, 11159, 11699, 12239

Offset

3,1

Comments

Run the PARI script savetwins(100000) or so to build the twinprime array of lower bounds before you run the main script.

Except for first term, same as A053778. - David Wasserman, Feb 22 2006

Links

Harvey P. Dale, Table of n, a(n) for n = 3..1000

Example

Twin prime pairs 5,7 and 11,13 contain only the composite numbers 6,7,8,9,10 between them. So 5 is in the table. 11,13 and 17,19 have no primes between.
11 is in the table. 41,43 and 59,61 have primes 47 and 53 between then so 41 is not listed.

Mathematica

Join[{3}, Select[Partition[Prime[Range[1500]], 4, 1], #[[4]]-#[[3]]==#[[2]]- #[[1]] == 2&][[All, 1]]] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(PARI) \save as twinpr.gp pbetweentw(n) = { forstep(x1=1, n, 2, c=0; t1 = twin[x1]; t2 = twin[x1+2]; for(y=t1+3, t2-1, if(isprime(y), c++) ); if(c==0, print1(t1", ")) ) } savetwins(n) = build a table of twin prime I want to upload a supporting file to store with the OEIS and add a link to it.lower bounds { twin = vector(n); c=1; forprime(x=3, n, if(isprime(x+2), twin[c]=x; c++; ) ) }

Crossrefs

Sequence in context: A168040 A068157 A062530 * A083841 A277552 A154941

Adjacent sequences: A089625 A089626 A089627 * A089629 A089630 A089631

Keyword

easy,nonn

Author

Cino Hilliard, Jan 01 2004

Status

approved