A335282 Lexicographically earliest strictly increasing sequence of positive integers whose Recamán transform has only distinct values.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset

1,2

Comments

The Recamán transform of a sequence {b(n), n>0} is the sequence {r(n), n>=0} defined as follows: r(0) = 0; for n > 0, r(n) = r(n-1) - b(n) if nonnegative and not already in the sequence, otherwise r(n) = r(n-1) + b(n).

This sequence has large runs of consecutive terms.

The Recamán transform of this sequence, say r, first differ from A064388 for n = 123: r(123) = 19 whereas A064388(123) = 300.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Recamán's sequence

Prog

(PARI) { rr = 2^r=0; for (v=1, 72, forstep (s=-1, +1, 2, if (r+s*v>=0 && !bittest(rr, r+s*v), rr += 2^r+=s*v; print1 (v ", "); break))) }

Crossrefs

Cf. A005132, A064388.

Sequence in context: A272076 A381611 A335280 * A381610 A370133 A351576

Adjacent sequences: A335279 A335280 A335281 * A335283 A335284 A335285

Keyword

nonn

Author

Rémy Sigrist, May 30 2020

Status

approved