Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Oct 24 2015 12:24:36
%S 5,7,11,13,15,16,17,19,21,23,27,29,31,33,35,36,37,39,41,43,45,47,51,
%T 53,55,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,79,
%U 80,81,82,83,85,86,87,88,89,90,91,92,93,94,95,97,98,99,100,101,102,103,105,106,107,109,110,111,112,113,114,115,116,117,118,119,121
%N Numbers n for which there exists x > n such that A155043(x) < A155043(n); numbers n for which A263078(n) is positive.
%H Antti Karttunen, <a href="/A263080/b263080.txt">Table of n, a(n) for n = 1..10000</a>
%e 5 is present, because if we start iterating A049820 from it as: A049820(5) = 3, A049820(3) = 1, A049820(1) = 0, we get a path of length 3 to reach zero, thus A155043(5) = 3. On the other hand, if we start from 6, the path is one step shorter: A049820(6) = 2, A049820(2) = 0 [i.e., A155043(6) = 2], thus there exists a number larger than 5 which results a shorter path to zero.
%t a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; Position[Table[k = 3 n; While[a@ k >= a@ n, k--]; k - n, {n, 121}], _Integer?Positive] // Flatten (* _Michael De Vlieger_, Oct 13 2015 *)
%o (PARI)
%o n=0; i=0; while(i < 10000, n++; if((A263077(n) > n), i++; write("b263080.txt",i," ",n)));
%o \\ Other code as in A263077.
%o (Scheme, with Antti Karttunen's IntSeq-library)
%o (define A263080 (MATCHING-POS 1 1 (COMPOSE positive? A263078)))
%Y Cf. A155043, A261089, A262503, A263077, A263078.
%Y Complement: A263079.
%K nonn
%O 1,1
%A _Antti Karttunen_, Oct 09 2015