Search: id:A111453
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%I A111453
%S A111453 1,5,9,3,7,11,2,6,10,4,8,12,16,20,14,18,22,13,17,21,15,19,23,27,31,25,
%T A111453 29,33,24,28,32,26,30,34,38,42,36,40,44,35,39,43,37,41,45,49,53,47,51,
%U A111453 55,46,50,54,48,52,56,60,64,58,62,66,57,61,65,59,63,67,71,75,69,73,77
%N A111453 a(1)=1; for n>1, a(n) is smallest positive integer not occurring earlier 
               in the sequence such that |a(n)-a(n-1)| is composite.
%C A111453 Sequence is a permutation of the positive integers.
%H A111453 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A111453 a(n)=n for n==1 (mod 11), a(n)=n+3 for n==2 (mod 11), a(n)=n+6 for n==3 
               (mod 11)
%F A111453 a(n)=n-1 for n==4 (mod 11), a(n)=n+2 for n==5 (mod 11), a(n)=n+5 for 
               n==6 (mod 11)
%F A111453 a(n)=n-5 for n==7 (mod 11), a(n)=n-2 for n==8 (mod 11), a(n)=n+1 for 
               n==9 (mod 11)
%F A111453 a(n)=n-6 for n==10 (mod 11) a(n)=n-3 for n==0 (mod 11). - Robert G. Wilson 
               v.
%e A111453 Among those positive integers not among the first 8 terms of the sequence 
               (4,8,10,12,...), a(9) = 10 is the lowest such that |a(9)-a(8)| = 
               |10-6| = 4 is a composite. (|8-6|=2 and |4-6|=2 are both primes. 
               So a(9) is not 4 or 8.)
%t A111453 f[n_] := Switch[Mod[n, 11], 0, n - 3, 1, n, 2, n + 3, 3, n + 6, 4, n 
               - 1, 5, n + 2, 6, n + 5, 7, n - 5, 8, n - 2, 9, n + 1, 10, n - 6]; 
               Array[a, 72] (* or *)
%t A111453 a[1] = 1; a[n_] := a[n] = Block[{k = 1, t = Table[a[i], {i, n - 1}]}, 
               While[Position[t, k] != {} || PrimeQ[k - a[n - 1]] || Abs[k - a[n 
               - 1]] == 1, k++ ]; k]; Array[a, 72] (* Robert G. Wilson v *)
%Y A111453 Cf. A002808.
%Y A111453 Sequence in context: A111698 A021948 A154265 this_sequence A153356 A129956 
               A010774
%Y A111453 Adjacent sequences: A111450 A111451 A111452 this_sequence A111454 A111455 
               A111456
%K A111453 nonn
%O A111453 1,2
%A A111453 Leroy Quet Nov 14 2005
%E A111453 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 17 2005

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