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A263080
Numbers n for which there exists x > n such that A155043(x) < A155043(n); numbers n for which A263078(n) is positive.
5
5, 7, 11, 13, 15, 16, 17, 19, 21, 23, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 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
OFFSET
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(PARI)
n=0; i=0; while(i < 10000, n++; if((A263077(n) > n), i++; write("b263080.txt", i, " ", n)));
\\ Other code as in A263077.
(Scheme, with Antti Karttunen's IntSeq-library)
(define A263080 (MATCHING-POS 1 1 (COMPOSE positive? A263078)))
CROSSREFS
Complement: A263079.
Sequence in context: A255363 A245757 A240912 * A280199 A196276 A079498
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 09 2015
STATUS
approved