A143345 - OEIS

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.

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 A349872 A087174

Adjacent sequences: A143342 A143343 A143344 * A143346 A143347 A143348

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jan 18 2011

STATUS

approved