A108065 Numbers n such that DENEAT(n!) is prime, where DENEAT(n) = concatenate number of even digits in n, number of odd digits and total number of digits.

1, 2, 3, 10, 15, 29, 35, 39, 51, 65, 167, 185, 198, 250, 282, 325, 366, 368, 382, 396, 400, 403, 450, 453, 509, 574, 575, 590, 598, 601, 699, 720, 759, 764, 788, 791, 797, 817, 824, 860, 863, 865, 867, 877, 901, 909, 911, 913, 930, 936, 1066, 1068, 1081, 1145

Offset: 1

Author

Jason Earls, Jun 03 2005

Keywords

• base
• nonn

Examples

			10 is in the sequence because 10! = 3628800 has 6 even digits, 1
odd digit and 7 total digits, yielding the prime 617.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073053.

Programs

Mathematica

eotQ[n_]:=Module[{idnf=IntegerDigits[n!],len,ev,od},len=Length[idnf];ev= Count[ idnf,?EvenQ];od=Count[idnf,?OddQ];PrimeQ[FromDigits[ Flatten[ IntegerDigits/@ Join[{ev,od,len}]]]]]; Select[Range[1200],eotQ] (* Harvey P. Dale, Jul 05 2017 *)