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 A143345 Lexicographically earliest sequence such that a(n) is coprime to the preceding 4 terms (or n-1 terms if n<5) and does not occur earlier. 3
 1, 2, 3, 5, 7, 11, 4, 9, 13, 17, 19, 8, 15, 23, 29, 31, 14, 25, 27, 37, 41, 16, 35, 33, 43, 47, 26, 49, 45, 53, 59, 22, 61, 21, 65, 67, 32, 71, 51, 55, 73, 28, 79, 39, 83, 85, 38, 77, 69, 89, 97, 10, 91, 57, 101, 103, 20, 107, 63, 109, 113, 34, 95, 81, 121, 127, 46, 119, 75, 131, 137, 44, 133, 87, 115, 139, 52, 149, 93, 125, 151, 56, 143, 111, 145, 157, 62, 161, 99, 163, 167, 40, 169, 123, 173, 179, 50, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS One possible extension of A084937, A103683 to N=4. Here, a(4)=5 is chosen such that a(n) is coprime to a(k) for 0 < k < n <= 4. Another choice is a(k)=k (k<=4), which yieds the different sequence A180348. It appears that: - no multiples of 6 occur in this sequence, so it is not a permutation of the integers. - a(n)=3 (mod 6)  iff  n=3, n=8, n=13 or n=14+5k, k>0. - a(n)=0 (mod 2) iff n= 2+5k, k>=0. - powers of 2 occur in natural order. - powers of 3 occur in natural order. - powers of any prime p occur in natural order. - powers of any number occur in natural order. LINKS Zak Seidov, Table of n, a(n) for n = 1..5000 PROG (PARI) print1("1, 2, 3"); a=[1, 2, 3, L=5]; unused=[4]; v=vector(#a, i, 1); for(n=4, 99, print1(", "a[#a]); for(i=1, #unused, apply(x->gcd(x, unused[i]), a)==v | next; a=concat(vecextract(a, "^1"), unused[i]); unused=vecextract(unused, Str("^", i)); next(2)); L++; while(apply(x->gcd(x, L), a) !=v, unused=concat(unused, L++-1); ); a=concat(vecextract(a, "^1"), L)) CROSSREFS Sequence in context: A097858 A084408 A257347 * A111679 A087174 A071963 Adjacent sequences:  A143342 A143343 A143344 * A143346 A143347 A143348 KEYWORD nonn AUTHOR M. F. Hasler, Jan 18 2011 STATUS approved

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Last modified January 21 03:00 EST 2021. Contains 340332 sequences. (Running on oeis4.)