A335299 - OEIS

%I #29 Jan 19 2021 21:57:18

%S 0,1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,42,

%T 17,43,16,44,15,45,14,46,79,113,78,114,77,39,78,38,79,37,80,36,81,35,

%U 82,34,83,33,84,32,85,31,86,30,27,85,26,86,147,209,146,210

%N a(0) = 0; for n > 0, a(n) = abs(a(n-1) - n) if not already in the sequence, otherwise a(n) = a(n-1) + n.

%C This sequence is a variant of Recamán's sequence (A005132).

%C This sequence first differ from A005132 for n = 57: a(57) = 27 whereas A005132(57) = 87.

%C Up to about 1.7 million terms the sequence values are concentrated along lines of integer gradient - see the image of the first 100000 terms. However beyond that each of these lines splits into two which subsequently cross and form a pattern reminiscent of a Cat's Cradle figure. See the linked images of the first 2 million and 20 million terms. - _Scott R. Shannon_, Jan 18 2021

%H Rémy Sigrist, <a href="/A335299/b335299.txt">Table of n, a(n) for n = 0..10000</a>

%H Scott R. Shannon, <a href="/A335299/a335299_1.png">Image of the first 2 million terms</a>. Note the splitting lines beyond about 1.7 million terms.

%H Scott R. Shannon, <a href="/A335299/a335299_2.png">Image of the first 20 million terms</a>.

%H Rémy Sigrist, <a href="/A335299/a335299.png">Colored scatterplot of the sequence for n = 0..100000</a> (where the color is function of round(a(n)/n) for n > 0)

%H Rémy Sigrist, <a href="/A335299/a335299_3.png">Scatterplot of the first 500000000 terms</a> (the plot alternates phases with losanges (Cat's Cradle figures) and phases with lines that radiate from the origin)

%H Rémy Sigrist, <a href="/A335299/a335299_4.png">Colored scatterplot of the first 2000000 terms</a> (the color changes in one direction or the other according to whether one passes from a(n) to abs(a(n)-n) or to a(n)+n, with an inversion with each bounce on the X axis)

%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>

%o (PARI) { rr = 0; r = 0; for (n=0, 64, if (!bittest(rr, m=abs(r-n)), r = m, r = r+n;); rr = bitor(rr, 2^r); print1 (r", ")) }

%Y Cf. A005132, A335300.

%K nonn

%O 0,3

%A _Rémy Sigrist_, May 31 2020