OFFSET
1,2
COMMENTS
The terms of A064736 lie on two (curved) lines; this is one of them.
To produce this set, start with S={1} and a counter c=2, then repeatedly add to S the element c*increment(c), where increment() adds 1 or 2 in case c+1 is already in S. - M. F. Hasler, May 23 2017
Alternate definition: {1} and numbers of the form m(m+1) if neither m nor m+1 is an earlier term, or (m-1)(m+1), if m > 1 is a term of the sequence. - M. F. Hasler, May 23 2017
By definition, complement of A286291. - David A. Corneth, May 25 2017
If the initial 1 is omitted, this is the complement of A121229. - N. J. A. Sloane, May 26 2017
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000
Ray Chandler, Table of n, a(n) for n = 1..1000000 (large gzipped file)
FORMULA
a(n) ~ n^2*(1 + 1.5/n^c) with c=1/2. (Conjectured, although for small n around 10^5 a smaller c ~ 0.478 is a better fit to the data.) - M. F. Hasler, May 23 2017
For n around 10^8, c ~ 0.4848 is a better fit. - David A. Corneth, May 25 2017
PROG
(PARI) A286290_list(Nmax, a=List(1), c=2)={while(#a<Nmax, listput(a, c*if(setsearch(a, c++), c++, c))); a} \\ M. F. Hasler, May 23 2017
(PARI) a(n) = my(r = 1); for(i = 2, n, r = nxt(r)); r
is(n) = if(n < 6, return(n==1)); if(issquare(n+1, &n), is(n), if(sqrtint(4*n+1)^2 == 4*n+1, s = sqrtint(4*n+1); !(is(s\2) || is(s\2+1)), return(0)))
nxt(n) = n==1&&return(6); if(issquare(n+1, &n), (n+1) * (n+2), my(m = sqrtint(n)); if(is(m + 2), (m + 1) * (m + 3), (m + 1) * (m + 2)))
lista(n) = my(c = 1, l = List([1])); for(i=2, n, c = nxt(c); listput(l, c)); l \\ David A. Corneth, May 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 23 2017
STATUS
approved