A336803 - OEIS

%I #34 Aug 27 2021 23:41:52

%S 3,6,9,12,15,19,22,26,30,34,38,43,47,51,56,60,65,70,75,79,84,89,94,99,

%T 104,110,115,120,125,130,136,141,147,152,158,163,169,174,180,185,191,

%U 197,202,208,214,220,225,231,237,243,249,255,261,267,273,279,285,291

%N Numbers k such that A230319(k) - A230319(k-1) = 2.

%C Sánchez Garza and Treviño proved the counting function for this sequence is asymptotic to x/log x. See link.

%H M. Sánchez Garza and E. Treviño, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Trevino/trevino6.html">On a sequence related to the factoradic representation of an integer</a>, Journal of Integer Sequences Vol. 24 (2021), Article 21.8.5.

%e 3 is a term because A230319(3) - A230319(2) = 2.

%t j[r_] := j[r] = Module[{k = 1}, While[k! <= k^(r - 1), k++]; k];

%t jPrimes = {}; Do[If[j[r + 1] - j[r] == 2, AppendTo[jPrimes, r], 0], {r, 1, 2500}]

%o (PARI) f(n) = my(k=1); while (k^n >= k!, k++); k; \\ A230319

%o isok(n) = f(n) - f(n-1) == 2; \\ _Michel Marcus_, Jan 27 2021

%Y Cf. A230319.

%K nonn

%O 1,1

%A _Enrique Treviño_, Jan 27 2021