A182278 - OEIS

%I #17 Apr 26 2012 11:34:10

%S 4,7,10,24,26,42,117,135,141,150,194,220,224,236,312,336,399,406,438,

%T 497,529,652,663,707,797,844,879,908,988,1092,1099,1133,1141,1300,

%U 1304,1371,1397,1494,1513,1536,1676,1886,1970,1981,1988,2076,2093,2221,2270,2356,2390,2462

%N Indices n such that A068869(n)<A068869(n-1).

%C The sequence A068869 is statistically growing, but I conjecture that there are infinitely many indices n such that A068869(n)<A068869(n-1). However, we don't yet know whether there are two consecutive integers in the sequence, i.e., a term n such that, additionally to the above, A068869(n+1)<A068869(n).

%C a(n) roughly grows like n^2.

%t w = 0; aa = {}; Do[k = Ceiling[Sqrt[n!]]^2 - n!;

%t If[k < w, AppendTo[aa, n - 1]]; w = k, {n, 1, 2500}]; aa

%o (PARI) for(i=1,2500,A068869(i)<A068869(i-1)&print1(i","))

%K nonn

%O 1,1

%A _M. F. Hasler_ and _Artur Jasinski_, Apr 23 2012