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

Author

N. J. A. Sloane, May 23 2017

Keywords

• nonn
• easy

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)

Crossrefs

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

Programs

PARI

A286290_list(Nmax,a=List(1),c=2)={while(#aM. 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

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