cp's OEIS Frontend

A159629 Slowest increasing sequence beginning with a(1)=4 such that A002828(a(n)) = A002828(n).

%I A159629 #11 Jul 29 2018 08:09:57
%S A159629 4,5,6,9,10,11,15,17,25,26,27,30,32,33,39,49,50,52,54,58,59,62,63,66,
%T A159629 81,82,83,87,89,91,92,97,99,101,102,121,122,123,124,125,128,129,131,
%U A159629 132,136,138,143,147,169,170,171,173,178,179,183,184,186,193,195,199,200,201,207
%N A159629 Slowest increasing sequence beginning with a(1)=4 such that A002828(a(n)) = A002828(n).
%C A159629 Conjecture: For every m>2 there exists a minimum index N(m) such that the minimal increasing recursive sequence S_m(n) beginning with m^2 with the condition A002828(S_m(n)) = A002828(n) coincides with a(n) for all n>N.
%H A159629 V. Shevelev, <a href="https://arxiv.org/abs/0904.2101">Several results on sequences which are similar to the positive integers</a> arXiv:0904.2101 [math.NT], 2009.
%F A159629 a(n+1) = min { l > a(n) : A002828(l) = A002828(n+1) }.
%t A159629 a2828[n_] := Which[SquaresR[1, n]>0, 1, SquaresR[2, n]>0, 2, SquaresR[3, n] > 0, 3, True, 4];
%t A159629 a[1] = 4; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[a2828[k] == a2828[n], Return[k]]];
%t A159629 Array[a, 63] (* _Jean-François Alcover_, Jul 28 2018 *)
%Y A159629 Cf. A002828, A159619, A159615, A007814, A004760, A159559, A159560.
%K A159629 nonn
%O A159629 1,1
%A A159629 _Vladimir Shevelev_, Apr 17 2009, May 04 2009
%E A159629 137 replaced by 136, extended by _R. J. Mathar_, Sep 17 2009