A335299 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.

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, 17, 43, 16, 44, 15, 45, 14, 46, 79, 113, 78, 114, 77, 39, 78, 38, 79, 37, 80, 36, 81, 35, 82, 34, 83, 33, 84, 32, 85, 31, 86, 30, 27, 85, 26, 86, 147, 209, 146, 210

Offset

0,3

Comments

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

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

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Scott R. Shannon, Image of the first 2 million terms. Note the splitting lines beyond about 1.7 million terms.

Scott R. Shannon, Image of the first 20 million terms.

Rémy Sigrist, Colored scatterplot of the sequence for n = 0..100000 (where the color is function of round(a(n)/n) for n > 0)

Rémy Sigrist, Scatterplot of the first 500000000 terms (the plot alternates phases with losanges (Cat's Cradle figures) and phases with lines that radiate from the origin)

Rémy Sigrist, Colored scatterplot of the first 2000000 terms (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)

Index entries for sequences related to Recamán's sequence

Prog

(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", ")) }

Crossrefs

Cf. A005132, A335300.

Sequence in context: A274648 A277558 A350578 * A005132 A064388 A064387

Adjacent sequences: A335296 A335297 A335298 * A335300 A335301 A335302

Keyword

nonn

Author

Rémy Sigrist, May 31 2020

Status

approved