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A079279
a(n)=n for n<=3; for n>3, a(n) is next integer sharing common factors with 1 or 2 of previous 3 terms.
2
1, 2, 3, 4, 8, 9, 10, 14, 15, 16, 21, 22, 26, 27, 28, 32, 33, 34, 38, 39, 40, 44, 45, 46, 51, 52, 56, 57, 58, 62, 63, 64, 68, 69, 70, 74, 75, 76, 81, 82, 86, 87, 88, 92, 93, 94, 98, 99, 100, 104, 105, 106, 111, 112, 116, 117, 118, 122, 123, 124, 128, 129, 130, 134, 135
OFFSET
1,2
COMMENTS
Does every sequence generated according to this rule, no matter which three initial terms are chosen, eventually fall into the same pattern with respect to the modulus 210 and thus have almost all of its terms in common with A079279?
Sequence includes all 3 mod 6 and 4 mod 6 numbers; all 2 mod 6 numbers except those congruent to 20 mod 30; all numbers congruent to 203 and 204 mod 210; and no other numbers except 1.
FORMULA
Conjectures from Colin Barker, Oct 15 2019: (Start)
G.f.: x*(1 + x + x^2 + x^3 + 4*x^4 + x^5 + x^6 + 4*x^7 + x^8 + x^9 + 5*x^10 + x^11 + 4*x^12 + x^13 + 3*x^15) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
a(n) = a(n-1) + a(n-14) - a(n-15) for n>16.
(End)
EXAMPLE
5, 6, 7 and 8 have factors in common with 0, 3, 0 and 2 (respectively) of terms a(2) through a(4) (2, 3 and 4); therefore a(5)=8.
CROSSREFS
Sequence in context: A246293 A047228 A032968 * A364381 A246444 A117847
KEYWORD
easy,nonn
AUTHOR
Matthew Vandermast, Feb 07 2003
STATUS
approved