

A111453


a(1)=1; for n>1, a(n) is smallest positive integer not occurring earlier in the sequence such that a(n)a(n1) is composite.


1



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, 29, 33, 24, 28, 32, 26, 30, 34, 38, 42, 36, 40, 44, 35, 39, 43, 37, 41, 45, 49, 53, 47, 51, 55, 46, 50, 54, 48, 52, 56, 60, 64, 58, 62, 66, 57, 61, 65, 59, 63, 67, 71, 75, 69, 73, 77
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OFFSET

1,2


COMMENTS

Sequence is a permutation of the positive integers.


LINKS

Table of n, a(n) for n=1..72.


FORMULA

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)
a(n)=n1 for n==4 (mod 11), a(n)=n+2 for n==5 (mod 11), a(n)=n+5 for n==6 (mod 11)
a(n)=n5 for n==7 (mod 11), a(n)=n2 for n==8 (mod 11), a(n)=n+1 for n==9 (mod 11)
a(n)=n6 for n==10 (mod 11) a(n)=n3 for n==0 (mod 11).  Robert G. Wilson v


EXAMPLE

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) = 106 = 4 is a composite. (86=2 and 46=2 are both primes. So a(9) is not 4 or 8.)


MATHEMATICA

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 *)
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 *)


CROSSREFS

Cf. A002808.
Sequence in context: A228402 A154265 A198133 * A222074 A245735 A303497
Adjacent sequences: A111450 A111451 A111452 * A111454 A111455 A111456


KEYWORD

nonn


AUTHOR

Leroy Quet, Nov 14 2005


EXTENSIONS

More terms from Robert G. Wilson v, Nov 17 2005


STATUS

approved



