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%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
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