cp's OEIS Frontend

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.

%I A071368 #20 Jan 14 2022 23:17:29
%S A071368 18362,2914913,5516281,6618242,7224834,9018353,9339114,10780554,
%T A071368 16831081,17800553,18164161,18646202,20239913,29743561,32464433,
%U A071368 32915513,42464514,43502033,45652314,51755761,53464314,62198634
%N 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.
%C A071368 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 A071368 A001221(a(n)) <= A001222(a(n)) <= 3. - _Reinhard Zumkeller_, Jul 31 2015
%H A071368 Reinhard Zumkeller, <a href="/A071368/b071368.txt">Table of n, a(n) for n = 1..100</a>
%e A071368 From _Reinhard Zumkeller_, Jul 31 2015: (Start)
%e A071368 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 A071368 5516281 is the smallest term also occurring in A071367:
%e A071368 5516281 + 0 = 1 * 5516281 = prime(381844) = a(3) = A071367(77);
%e A071368 5516281 + 1 = 2 * 2758141 = 2 * prime(200537);
%e A071368 5516281 + 2 = 3 * 1838761 = 3 * prime(137758);
%e A071368 5516281 + 3 = 4 * 1379071 = 4 * prime(105622);
%e A071368 5516281 + 4 = 5 * 1103257 = 5 * prime(85955);
%e A071368 5516281 + 5 = 6 * 919381 = 6 * prime(72692), not needed for A071367.
%e A071368 (End)
%o A071368 (Haskell)
%o A071368 a071368 n = a071368_list !! (n-1)
%o A071368 a071368_list = filter f [1..] where
%o A071368    f x = and $ map g [6, 5 .. 1] where
%o A071368      g k = sum (map h $ map (+ x) [0..5]) == 1 where
%o A071368        h z = if r == 0 then a010051' z' else 0
%o A071368              where (z', r) = divMod z k
%o A071368 -- _Reinhard Zumkeller_, Jul 31 2015
%Y A071368 Cf. A071367 - A071373.
%Y A071368 Cf. A010051, A001221, A001222.
%K A071368 nonn
%O A071368 1,1
%A A071368 _Don Reble_, May 21 2002