A286290 A bisection of A064736.

1, 6, 12, 20, 35, 56, 72, 90, 110, 143, 182, 210, 240, 272, 306, 342, 399, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1224, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550, 2652, 2756, 2862, 2970, 3135, 3306, 3422, 3540

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

Cf. A064736, A286291, A286292, A286293, A121229.

Sequence in context: A295904 A309836 A117343 * A240521 A366928 A220211

Adjacent sequences: A286287 A286288 A286289 * A286291 A286292 A286293

Keyword

nonn,easy

Author

N. J. A. Sloane, May 23 2017

Status

approved