cp's OEIS Frontend

A292523 Decimal encoding T(n,k) of the k-th non-averaging permutation of [n]; triangle T(n,k), n >= 0, k = 1..A003407(n), read by rows.

%I A292523 #42 Feb 16 2025 08:33:51
%S A292523 0,1,12,21,132,213,231,312,1324,1342,2143,2413,2431,3124,3142,3412,
%T A292523 4213,4231,15324,15342,21453,24153,24315,24351,24513,31254,31524,
%U A292523 31542,35124,35142,35412,42153,42315,42351,42513,45213,51324,51342,153264,153426,153462
%N A292523 Decimal encoding T(n,k) of the k-th non-averaging permutation of [n]; triangle T(n,k), n >= 0, k = 1..A003407(n), read by rows.
%C A292523 A non-averaging permutation avoids any 3-term arithmetic progression.
%C A292523 The encoding of the empty permutation () is 0. For positive n each element in the permutation is encoded using 1+floor(log_10(n)) = A055642(n) digits with leading 0's if necessary. Then all elements are concatenated.
%C A292523 All terms are in increasing order.
%H A292523 Alois P. Heinz, <a href="/A292523/b292523.txt">Rows n = 0..14, flattened</a>
%H A292523 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonaveragingSequence.html">Nonaveraging Sequence</a>
%H A292523 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%H A292523 <a href="/index/No#non_averaging">Index entries related to non-averaging sequences</a>
%e A292523 Triangle T(n,k) begins:
%e A292523 :            0;
%e A292523 :            1;
%e A292523 :           12, 21;
%e A292523 :          132, 213, 231, 312;
%e A292523 :         1324, 1342, 2143, 2413,  2431,    3124,  3142, 3412, 4213, 4231;
%e A292523 :        15324, 15342, 21453, 24153,    ...,    42513, 45213, 51324, 51342;
%e A292523 :       153264, 153426, 153462, 153624, ..., 624153, 624315, 624351, 624513;
%e A292523 :      1532764, 1537264, 1537426,       ...,       7351462, 7351624, 7356124;
%e A292523 :     15327648, 15327684, 15372648,     ...,     84627351, 84672315, 84672351;
%e A292523 :    195327648, 195327684, 195372648,   ...,   915738462, 915783426, 915783462;
%e A292523 :   1090503020710060408,                ...,               10020608090401050703;
%e A292523 :  109050302110710060408,               ...,              1103070910010502060804;
%e A292523 : 10905031107021006041208,              ...,             120408100206110307090105;
%p A292523 T:= proc(n) option remember; local b, l, c; b, l, c:=
%p A292523       proc(s, p) local ok, i, j, k;
%p A292523         if nops(s) = 0 then l:= [l[], parse(p)]
%p A292523       else for j in s do ok, i, k:= true, j-1, j+1;
%p A292523              while ok and i>0 and k<=n do ok, i, k:=
%p A292523                not i in s xor k in s, i-1, k+1 od;
%p A292523              `if`(ok, b(s minus {j}, cat(p, 0$(c-length(j)), j)), 0)
%p A292523            od
%p A292523         fi
%p A292523       end, [], length(n); b({$1..n}, "0"): sort(l)[]
%p A292523     end:
%p A292523 seq(T(n), n=0..6);
%Y A292523 Cf. A003407, A030299, A055642, A088370.
%K A292523 nonn,tabf,base
%O A292523 0,3
%A A292523 _Alois P. Heinz_, Dec 08 2017