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

Author

Rémy Sigrist, May 30 2020

Keywords

• nonn

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

Crossrefs

Cf. A005132, A064388.

Programs

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))) }