A071368 Numbers k such that k+0, k+1, k+2, k+3, k+4, and k+5 are, in some order, 1 * a prime, 2 * a prime, ... and 6 * a prime.

18362, 2914913, 5516281, 6618242, 7224834, 9018353, 9339114, 10780554, 16831081, 17800553, 18164161, 18646202, 20239913, 29743561, 32464433, 32915513, 42464514, 43502033, 45652314, 51755761, 53464314, 62198634

Offset: 1

Author

Don Reble, May 21 2002

Keywords

• nonn

Comments

The terms ending in the digit "1" are primes congruent to 1 (mod 120), which form the sequence A208455: See there for a proof. - M. F. Hasler, Feb 27 2012

A001221(a(n)) <= A001222(a(n)) <= 3. - Reinhard Zumkeller, Jul 31 2015

Examples

			From _Reinhard Zumkeller_, Jul 31 2015: (Start)
18362 is in the sequence because 18362=2*9181, 18363=3*6121, 18364=4*4591, 18365=5*3673, 18366=6*3061 and 18367=1*18367. The left factors are the integers 1 to 6; and the right factors are primes.
5516281 is the smallest term also occurring in A071367:
5516281 + 0 = 1 * 5516281 = prime(381844) = a(3) = A071367(77);
5516281 + 1 = 2 * 2758141 = 2 * prime(200537);
5516281 + 2 = 3 * 1838761 = 3 * prime(137758);
5516281 + 3 = 4 * 1379071 = 4 * prime(105622);
5516281 + 4 = 5 * 1103257 = 5 * prime(85955);
5516281 + 5 = 6 * 919381 = 6 * prime(72692), not needed for A071367.
(End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A071367 - A071373.

Cf. A010051, A001221, A001222.

Programs

Haskell

a071368 n = a071368_list !! (n-1)
a071368_list = filter f [1..] where
   f x = and $ map g [6, 5 .. 1] where
     g k = sum (map h $ map (+ x) [0..5]) == 1 where
       h z = if r == 0 then a010051' z' else 0
             where (z', r) = divMod z k
-- Reinhard Zumkeller, Jul 31 2015