cp's OEIS Frontend

A220280 The reluctant sequence for A002260.

%I A220280 #38 Jun 07 2024 14:07:24
%S A220280 1,1,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,2,1,2,3,1,1,2,1,2,3,1,1,1,2,1,2,3,
%T A220280 1,2,1,1,2,1,2,3,1,2,3,1,1,2,1,2,3,1,2,3,4,1,1,2,1,2,3,1,2,3,4,1,1,1,
%U A220280 2,1,2,3,1,2,3,4,1,2,1,1,2,1,2,3,1,2,3,4,1,2,3
%N A220280 The reluctant sequence for A002260.
%C A220280 The reluctant sequence B for a sequence A is a triangular array in which row k (>= 1) consists of the first k terms of A.
%C A220280 Here A002260 is the reluctant sequence for the sequence 1,2,3,... of positive numbers (A000027).
%H A220280 Boris Putievskiy, <a href="/A220280/b220280.txt">Table of n, a(n) for n = 1..10000</a>
%H A220280 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A220280 a(n) = n1 - t1(t1+1)/2, where n1 = n - t(t+1)/2, t1 = floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2]. For example, a(6)=2 since t=2, t1=1, n1=3.
%e A220280 A002260 begins
%e A220280   1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, ...
%e A220280 so the first few rows of the new triangle are
%e A220280    1,
%e A220280    1, 1,
%e A220280    1, 1, 2,
%e A220280    1, 1, 2, 1,
%e A220280    1, 1, 2, 1, 2,
%e A220280    1, 1, 2, 1, 2, 3,
%e A220280    ...
%e A220280                                                                                ~
%o A220280 (Python)
%o A220280 t=int((math.sqrt(8*n-7) - 1)/ 2)
%o A220280 n1=n-t*(t+1)/2
%o A220280 t1=int((math.sqrt(8*n1-7) - 1)/ 2)
%o A220280 a=n1-t1*(t1+1)/2
%Y A220280 Cf. A002260, A002262, A037126, A059268, A215026.
%K A220280 easy,nonn,tabl
%O A220280 1,6
%A A220280 _Boris Putievskiy_, Dec 12 2012
%E A220280 Edited by _N. J. A. Sloane_, Jun 07 2024