A308125 Numbers k that are a multiple of the DENEAT operator applied to k (A073053).

0, 22, 44, 66, 88, 123, 264, 369, 462, 615, 660, 738, 759, 852, 957, 1120, 1344, 1568, 1884, 2024, 2068, 2200, 2244, 2288, 2420, 2464, 2640, 2684, 2860, 2912, 3350, 3360, 3584, 3752, 4004, 4048, 4224, 4268, 4400, 4444, 4488, 4620, 4664, 4840, 4884, 5024, 6028, 6204

Offset: 0

Author

Paolo P. Lava, May 14 2019

Keywords

• nonn
• base
• easy

Comments

The DENEAT operator is also known as the Sisyphus function.

On the other hand, the sequence of numbers k such that DENEAT(k) is a multiple of k, is the finite sequence {1, 11, 14, 16, 22, 56, 123}.

Examples

			2912 / DENEAT(2912) = 2912 / 224 = 13.
		

References

• J. Schram, The Sisyphus string, J. Rec. Math., 19:1 (1987), 43-44.

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A073053, A073054.

Programs

Maple

P:=proc(n) local a,b,c,d,k; a:=convert(n,base,10); b:=0: c:=0:
for k from 1 to nops(a) do if a[k] mod 2=0 then b:=b+1; else c:=c+1; fi;
od: d:=b*10^length(c)+c; a:=n/(d*10^length(length(n))+length(n)):
if frac(a)=0 then n; fi; end: 0,seq(P(i),i=1..6204);