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

Author

Ki Punches, May 13 2009

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A046132, A160370

Programs

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 *)

Formula

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

Extensions

Edited by R. J. Mathar, May 14 2009