A344538 Lexicographically earliest sequence such that |a(n+1)-a(n)| is a cube > 1 and no number occurs twice; a(0) = 0.

0, 8, 16, 24, 32, 5, 13, 21, 29, 2, 10, 18, 26, 34, 7, 15, 23, 31, 4, 12, 20, 28, 1, 9, 17, 25, 33, 6, 14, 22, 30, 3, 11, 19, 27, 35, 43, 51, 59, 67, 40, 48, 56, 64, 37, 45, 53, 61, 69, 42, 50, 58, 66, 39, 47, 55, 63, 36, 44, 52, 60, 68, 41, 49, 57, 65, 38

Offset

0,2

Comments

The difference between successive terms, a(n+1)-a(n), is either +8 or -27. This sequence is a permutation of the nonnegative integers (with no "gaps").

Links

Table of n, a(n) for n=0..66.

Mike Koss, Derivation and proof.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,-1,2,-1,0,0,0,0,-1,2,-1,0,0,0,0,-1,2,-1,0,0,0,0,-1,2,-1).

Index entries for sequences that are permutations of the nonnegative integers

Formula

a(n+35) = a(n) + 35 for all n.

a(n) = 2*a(n-1) - a(n-2) - a(n-7) + 2*a(n-8) - a(n-9) - a(n-14) + 2*a(n-15) - a(n-16) - a(n-21) + 2*a(n-22) - a(n-23) - a(n-28) + 2*a(n-29) - a(n-30) for n > 29. - Stefano Spezia, May 23 2021

Mathematica

a[0]=0; a[n_]:=a[n]=(k=1; While[!IntegerQ[s=Abs[k-a[n-1]]^(1/3)]||s==1||MemberQ[Array[a, n-1], k], k++]; k); Array[a, 100, 0] (* Giorgos Kalogeropoulos, May 27 2021 *)

Crossrefs

Cf. A277616.

Sequence in context: A177899 A358727 A246311 * A244371 A144566 A037989

Adjacent sequences: A344535 A344536 A344537 * A344539 A344540 A344541

Keyword

nonn,easy

Author

Mike Koss, May 22 2021

Status

approved