A160440 Smaller member of a pair (p,q) of cousin primes such that p and q are in different centuries.

97, 397, 499, 1297, 1597, 1999, 2797, 3697, 4999, 6199, 6997, 7699, 9199, 10099, 10597, 12097, 13099, 16699, 18397, 20899, 21397, 21499, 21799, 23197, 23599, 25999, 26497, 27697, 27799, 27997, 32299, 32797, 33199, 34297, 35797, 38197, 38299, 39499, 42697

Offset

1,1

Comments

Sequence is probably infinite.

Dickson's conjecture implies there are infinitely many pairs of primes (100*k-3, 100*k+1) and infinitely many pairs of primes (100*k-1, 100*k+3). - Robert Israel, Mar 28 2023

It appears that every integer occurs as the difference round((a(n+1)-a(n))/100); all numbers 1..298 occur as these differences for a(n) < 1000000000. - Hartmut F. W. Hoft, May 18 2017

Links

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

Formula

{A023200(n): [A023200(n)/100] <> [A046132(n)/100]}, where [..]=floor(..).

Example

Cousin primes 1597 and 1601 are in successive (that is 16th and 17th) centuries.

Maple

R:= NULL: count:= 0:
for i from 1 while count < 100 do
  if ((i mod 3 = 1) and isprime(100*i-3) and isprime(100*i+1)) then
     R:= R, 100*i-3; count:= count+1
  elif ((i mod 3 = 2) and isprime(100*i-1) and isprime(100*i+3)) then
     R:= R, 100*i-1; count:= count+1
fi od:
R; # Robert Israel, Mar 28 2023

Mathematica

a160440[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[100, n, 100]], First[#]-Last[#]==4&]]
a160440[43000] (* data *) (* Hartmut F. W. Hoft, May 18 2017 *)

Crossrefs

Cf. A046132, A160370

Sequence in context: A031927 A174338 A050666 * A107213 A157331 A142834

Adjacent sequences: A160437 A160438 A160439 * A160441 A160442 A160443

Keyword

nonn

Author

Ki Punches, May 13 2009

Extensions

Edited by R. J. Mathar, May 14 2009

Status

approved