A071368 - OEIS

%I #20 Jan 14 2022 23:17:29

%S 18362,2914913,5516281,6618242,7224834,9018353,9339114,10780554,

%T 16831081,17800553,18164161,18646202,20239913,29743561,32464433,

%U 32915513,42464514,43502033,45652314,51755761,53464314,62198634

%N 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.

%C 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

%C A001221(a(n)) <= A001222(a(n)) <= 3. - _Reinhard Zumkeller_, Jul 31 2015

%H Reinhard Zumkeller, <a href="/A071368/b071368.txt">Table of n, a(n) for n = 1..100</a>

%e From _Reinhard Zumkeller_, Jul 31 2015: (Start)

%e 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.

%e 5516281 is the smallest term also occurring in A071367:

%e 5516281 + 0 = 1 * 5516281 = prime(381844) = a(3) = A071367(77);

%e 5516281 + 1 = 2 * 2758141 = 2 * prime(200537);

%e 5516281 + 2 = 3 * 1838761 = 3 * prime(137758);

%e 5516281 + 3 = 4 * 1379071 = 4 * prime(105622);

%e 5516281 + 4 = 5 * 1103257 = 5 * prime(85955);

%e 5516281 + 5 = 6 * 919381 = 6 * prime(72692), not needed for A071367.

%e (End)

%o (Haskell)

%o a071368 n = a071368_list !! (n-1)

%o a071368_list = filter f [1..] where

%o    f x = and $ map g [6, 5 .. 1] where

%o      g k = sum (map h $ map (+ x) [0..5]) == 1 where

%o        h z = if r == 0 then a010051' z' else 0

%o              where (z', r) = divMod z k

%o -- _Reinhard Zumkeller_, Jul 31 2015

%Y Cf. A071367 - A071373.

%Y Cf. A010051, A001221, A001222.

%K nonn

%O 1,1

%A _Don Reble_, May 21 2002