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A094766 Trajectory of 11 under repeated application of the map n -> n + 2*square excess of n (see A094765). 2
11, 15, 27, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343, 381, 421, 463, 507, 553, 601, 651, 703, 757, 813, 871, 931, 993, 1057, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893, 1981, 2071, 2163, 2257, 2353, 2451, 2551, 2653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The trajectory of 3 gives A002061 and 5 gives essentially the same trajectory as 3.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

S. H. Weintraub, An interesting recursion, Amer. Math. Monthly, 111 (No. 6, 2004), 528-530.

FORMULA

Numbers given satisfy a(n) = n^2 + 5n + 7, for n>2. - Ralf Stephan, Dec 04 2004

From Robert Israel, Oct 23 2015: (Start)

This is because for x = m^2 + 5*m + 7, (m+2)^2 < x < (m+3)^2 so A094765(x) = x + 2*(x-(m+2)^2) = m^2 + 7*m + 13 = (m+1)^2 + 5*(m+1) + 7.

Similarly, for any positive integer k, the trajectory of k^2 + k + 1 is n^2 + (2k+1) n + k^2 + k + 1 for n >= 0.

G.f.: 4 + 2*x + 6*x^2 + (7-8*x+3*x^2)/(1-x)^3. (End)

MAPLE

f:= n -> 3*n - 2*floor(sqrt(n))^2:

g:= proc(n) option remember; f(procname(n-1)) end proc:

g(0):= 11:

seq(g(n), n=0..100); # Robert Israel, Oct 23 2015

PROG

(PARI) lista(nn) = {print1(n=11, ", "); for (k=2, nn, m = 3*n - 2*sqrtint(n)^2; print1(m, ", "); n = m; ); } \\ Michel Marcus, Oct 23 2015

(PARI) Vec(4+2*x+6*x^2+(7-8*x+3*x^2)/(1-x)^3 + O(x^100)) \\ Altug Alkan, Oct 23 2015

CROSSREFS

Cf. A002061, A053186, A094765.

Sequence in context: A256498 A054280 A214863 * A009407 A009433 A275242

Adjacent sequences:  A094763 A094764 A094765 * A094767 A094768 A094769

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 10 2004

STATUS

approved

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Last modified May 21 14:50 EDT 2019. Contains 323443 sequences. (Running on oeis4.)