A079358 a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is not a multiple of either 3 or 4.".

1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14, 17, 19, 22, 24, 27, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 46, 47, 49, 50, 53, 54, 55, 58, 60, 61, 62, 65, 67, 70, 72, 75, 77, 79, 80, 82, 83, 84, 87, 89, 91, 94, 96, 99, 101, 102, 103, 106, 107, 108, 111, 113

Offset

1,2

Comments

A generalization of A079000 that, like A079000 itself, is based on a class of numbers comprising exactly one-half of the integers.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2. See also arXiv:math/0305308 [math.NT], 2003.

Example

a(3) cannot be 3 because that would imply that the third term is not a multiple of 3. 4 is the smallest possible value for a(3) that creates no contradiction; therefore a(3)=4 and the fourth term is the next member of the sequence that is not a multiple of 3 or 4.

Mathematica

Block[{c, k, nn, s}, nn = 2^16; c[_] := False; k = 1; c[1] = True; s = {0, 3, 4, 6, 8, 9}; {1}~Join~Reap[Do[k++; Which[c[n], While[MemberQ[s, Mod[k, 12]], k++], k == n, If[MemberQ[s, Mod[k, 12]], k++], True, While[FreeQ[s, Mod[k, 12]], k++] ]; Sow[k]; c[k] = True, {n, 2, nn}] ][[-1, 1]] ] (* Michael De Vlieger, Aug 10 2025 *)

Crossrefs

Cf. A079000.

Sequence in context: A254792 A062102 A092289 * A184014 A183856 A183869

Adjacent sequences: A079355 A079356 A079357 * A079359 A079360 A079361

Keyword

easy,nonn

Author

Matthew Vandermast, Feb 14 2003

Extensions

a(42) onward corrected by Sean A. Irvine, Aug 10 2025

Status

approved