A162023 Exactly 10 consecutive odd integers starting with n are composite.

1131, 1341, 1673, 1953, 2183, 2313, 2483, 2559, 2979, 3143, 3231, 3279, 3471, 3741, 3969, 4029, 4181, 4307, 4527, 4763, 4841, 5127, 5241, 5361, 5451, 5537, 5603, 5759, 5961, 6177, 6401, 6429, 6501, 6741, 6927, 7083, 7131, 7263, 7373, 7769, 7797, 7973

Offset: 1

Author

Zak Seidov, Jun 25 2009, typo corrected Aug 14 2009

Keywords

• nonn

Examples

			Exactly 10 consecutive odd integers 1131(2)1149 are composite while 1151 is prime.
		

Links

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

Crossrefs

Cf. A162022, A014076, A071904.

Programs

Maple

R:= NULL: count:= 0: k:= 1: state:= 0:
while count < 100 do
  k:= k+2;
  if isprime(k) then
    if state >= 10 then R:= R,k - 20; count:= count + 1;  fi;
    state:= 0;
  else state:= state + 1
  fi;
od:
R; # Robert Israel, Feb 12 2025

Mathematica

Transpose[Select[Partition[Range[1,8001,2],11,1],PrimeQ/@ == {False,False,False,False,False,False,False,False,False,False,True}&]] [[1]] (* Harvey P. Dale, Nov 21 2011 *)