cp's OEIS Frontend

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.".

%I A079358 #16 Aug 11 2025 10:30:29
%S A079358 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,
%T A079358 40,41,42,43,46,47,49,50,53,54,55,58,60,61,62,65,67,70,72,75,77,79,80,
%U A079358 82,83,84,87,89,91,94,96,99,101,102,103,106,107,108,111,113
%N 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.".
%C A079358 A generalization of A079000 that, like A079000 itself, is based on a class of numbers comprising exactly one-half of the integers.
%H A079358 Michael De Vlieger, <a href="/A079358/b079358.txt">Table of n, a(n) for n = 1..10000</a>
%H A079358 Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2. See also <a href="http://arXiv.org/abs/math.NT/0305308">arXiv:math/0305308</a> [math.NT], 2003.
%e A079358 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.
%t A079358 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 *)
%Y A079358 Cf. A079000.
%K A079358 easy,nonn
%O A079358 1,2
%A A079358 _Matthew Vandermast_, Feb 14 2003
%E A079358 a(42) onward corrected by _Sean A. Irvine_, Aug 10 2025