A336803 Numbers k such that A230319(k) - A230319(k-1) = 2.

3, 6, 9, 12, 15, 19, 22, 26, 30, 34, 38, 43, 47, 51, 56, 60, 65, 70, 75, 79, 84, 89, 94, 99, 104, 110, 115, 120, 125, 130, 136, 141, 147, 152, 158, 163, 169, 174, 180, 185, 191, 197, 202, 208, 214, 220, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285, 291

Offset: 1

Author

Enrique Treviño, Jan 27 2021

Keywords

• nonn

Comments

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

Examples

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

Links

• M. Sánchez Garza and E. Treviño, On a sequence related to the factoradic representation of an integer, Journal of Integer Sequences Vol. 24 (2021), Article 21.8.5.

Crossrefs

Cf. A230319.

Programs

Mathematica

j[r_] := j[r] = Module[{k = 1}, While[k! <= k^(r - 1), k++]; k];
jPrimes = {}; Do[If[j[r + 1] - j[r] == 2, AppendTo[jPrimes, r], 0], {r, 1, 2500}]

PARI

f(n) = my(k=1); while (k^n >= k!, k++); k; \\ A230319
isok(n) = f(n) - f(n-1) == 2; \\ Michel Marcus, Jan 27 2021