A202706 Numbers k such that (sum of digits of k!) / 9 is prime.

9, 10, 12, 13, 14, 15, 16, 17, 19, 21, 23, 30, 36, 37, 45, 52, 53, 54, 55, 56, 63, 67, 71, 78, 82, 84, 88, 89, 94, 98, 101, 106, 109, 110, 124, 126, 127, 131, 132, 137, 139, 141, 144, 146, 170, 175, 195, 199, 224, 255, 263, 267, 270, 271, 276, 277, 278, 281

Offset: 1

Author

Michel Lagneau, Dec 23 2011

Keywords

• nonn
• base
• changed

Comments

Numbers k such that A004152(k)/9 is prime.

If k > 5, then (sum of digits of k!) / 9 is an integer (see A004152).

Examples

			10 is in the sequence because 10!= 3628800 and (3+6+2+8+8)/9 = 27/9 = 3 is prime.
		

Crossrefs

Cf. A000142, A004152.

Programs

Mathematica

lst={}; Do[If[PrimeQ[Sum[DigitCount[n!][[i]]*i/9,{i,1,9}]], AppendTo[lst, n]], {n, 300}]; lst