A071367 Numbers n such that n+0, n+1, n+2, n+3 and n+4 are, in some order, 1 * a prime, 2 * a prime, 3 * a prime, 4 * a prime and 5 * a prime.

6, 211, 2305, 2731, 19441, 116131, 174595, 222931, 229945, 232051, 243091, 266401, 334315, 350785, 423481, 495265, 523945, 530545, 535915, 539401, 556705, 600601, 663601, 671035, 689131, 721891, 907195, 908041, 1105105, 1113961, 1289731

Offset: 1

Author

Don Reble, May 21 2002

Keywords

• nonn

Comments

A001221(a(n)) <= 2; A001222(a(n)) <= 3. - Reinhard Zumkeller, Aug 01 2015

Examples

			211 is a term because 211=1*211, 212=4*53, 213=3*71, 214=2*107 and 215=5*43. The left factors are the integers 1 to 5; and the right factors are primes.
6 is a term because 6=2*3, 7=1*7, 8=4*2, 9=3*3, 10=5*2 where the left factors are the integers 1 to 5 and the right factors are primes. - _Sean A. Irvine_, Jul 14 2024
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A071367 - A071373.

Cf. A010051, A001221, A001222.

Programs

Haskell

a071367 n = a071367_list !! (n-1)
a071367_list = tail $ filter f [1..] where
   f x = and $ map g [5, 4 .. 1] where
     g k = sum (map h $ map (+ x) [0..4]) == 1 where
       h z = if r == 0 then a010051' z' else 0
             where (z', r) = divMod z k
-- Reinhard Zumkeller, Jul 31 2015

Extensions

Missing 6 inserted by Sean A. Irvine, Jul 14 2024