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

Author

Rémy Sigrist, May 31 2020

Keywords

• nonn

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

Crossrefs

Cf. A005132, A335300.

Programs

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", ")) }