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A220465 Reverse reluctant sequence of reverse reluctant sequence A004736.

%I A220465 #20 Feb 16 2022 11:59:04
%S A220465 1,2,1,1,2,1,3,1,2,1,2,3,1,2,1,1,2,3,1,2,1,4,1,2,3,1,2,1,3,4,1,2,3,1,
%T A220465 2,1,2,3,4,1,2,3,1,2,1,1,2,3,4,1,2,3,1,2,1,5,1,2,3,4,1,2,3,1,2,1,4,5,
%U A220465 1,2,3,4,1,2,3,1,2,1,3,4,5,1,2,3,4,1,2,3,1,2,1,2,3,4,5,1,2,3,4,1,2,3,1,2,1,1,2,3,4,5,1,2,3,4,1,2,3,1,2,1,6,1,2,3
%N A220465 Reverse reluctant sequence of reverse reluctant sequence A004736.
%C A220465 Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.
%C A220465 Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
%C A220465 Sequence A004736 is the reverse reluctant sequence of sequence 1,2,3,... (A000027).
%H A220465 Boris Putievskiy, <a href="/A220465/b220465.txt">Rows n = 1..140 of triangle, flattened</a>
%H A220465 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A220465 T(n,k) = A004736(n-k+1).
%F A220465 As a linear array, the sequence is a(n) = (t1*t1+3*t1+4)/2-n1, where n1=(t*t+3*t+4)/2-n, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].
%e A220465 The start of the sequence as triangle array T(n,k) is:
%e A220465   1;
%e A220465   2,1;
%e A220465   1,2,1;
%e A220465   3,1,2,1;
%e A220465   2,3,1,2,1;
%e A220465   1,2,3,1,2,1;
%e A220465   ...
%o A220465 (Python)
%o A220465 t=int((math.sqrt(8*n-7) - 1)/ 2)
%o A220465 n1=(t*t+3*t+4)/2-n
%o A220465 t1=int((math.sqrt(8*n1-7) - 1)/ 2)
%o A220465 m=(t1*t1+3*t1+4)/2-n1
%Y A220465 Cf. A000027, A004736, A002260, A220280.
%K A220465 easy,nonn,tabl
%O A220465 1,2
%A A220465 _Boris Putievskiy_, Dec 15 2012