A263080 Numbers n for which there exists x > n such that A155043(x) < A155043(n); numbers n for which A263078(n) is positive.

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

Antti Karttunen, Table of n, a(n) for n = 1..10000

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

Cf. A155043, A261089, A262503, A263077, A263078.

Complement: A263079.

Sequence in context: A255363 A245757 A240912 * A280199 A196276 A079498

Adjacent sequences: A263077 A263078 A263079 * A263081 A263082 A263083

Keyword

nonn

Author

Antti Karttunen, Oct 09 2015

Status

approved