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
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
KEYWORD
nonn
AUTHOR
Ki Punches, May 13 2009
EXTENSIONS
Edited by R. J. Mathar, May 14 2009
STATUS
approved