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

Author

Antti Karttunen, Oct 09 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Complement: A263079.

Programs

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 *)

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)))