# A026472/4/6 help needed

Ralf Stephan ralf at ark.in-berlin.de
Sun Nov 21 11:42:32 CET 2004

```Hello alii,

the definitions of sequences A026472,A026474,A026476 do not match
the numbers. I'm referring to the bit
a(n) = least positive integer > a(n-1) and not a(i)+a(j)+a(k) for
1<=i<=j<=k<=n.

While A026474 is well-defined through the term '3-Stöhr-sequence'[*],
and can thus be reconstructed, there seems no way to get the author's
algorithm for the others. Prof Kimberling himself tried. So, without
seqfan's help, the only definitions left are my accompanying conjectures.

Can you construct a kind of sum-free sequence matching A026472 or A026476?

%I A026472
%S A026472 1,2,3,7,13,14,25,26,37,38,49,50,61,62,73,74,85,86,97,98,109,
%T A026472 110,121,122,133,134,145,146,157,158
%F A026472 {3, 7} and congruent to {1, 2} mod 12 (conjectured). - R. Stephan, May 12 2004

%I A026476
%S A026476 1,3,4,9,12,23,26,37,40,51,54,65,68,79,82,93,96,107,110,121,124,
%T A026476 135,138,149,152,163,166,177,180,191
%F A026476 For n>3, a(n) = 7n - 21 + 2(-1)^n (conjectured). - R. Stephan, Apr 30 2004

Sincerely,
ralf
[*] a corrected definition would be
%N A026474 a(n) = least positive integer > a(n-1) and not a(i)+a(j) or a(i)+a(j)+a(k) for 1<=i<j<k<n (a 3-Stohr sequence).

```