A182278 Indices n such that A068869(n)<A068869(n-1).

4, 7, 10, 24, 26, 42, 117, 135, 141, 150, 194, 220, 224, 236, 312, 336, 399, 406, 438, 497, 529, 652, 663, 707, 797, 844, 879, 908, 988, 1092, 1099, 1133, 1141, 1300, 1304, 1371, 1397, 1494, 1513, 1536, 1676, 1886, 1970, 1981, 1988, 2076, 2093, 2221, 2270, 2356, 2390, 2462

Offset: 1

Author

M. F. Hasler and Artur Jasinski, Apr 23 2012

Keywords

• nonn

Comments

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).

a(n) roughly grows like n^2.

Programs

Mathematica

w = 0; aa = {}; Do[k = Ceiling[Sqrt[n!]]^2 - n!;
If[k < w, AppendTo[aa, n - 1]]; w = k, {n, 1, 2500}]; aa

PARI

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