A202709 (Sum of digits of n!!) / 9.

2, 2, 2, 2, 2, 2, 4, 5, 5, 4, 5, 5, 4, 6, 7, 5, 8, 5, 8, 8, 10, 10, 10, 9, 12, 9, 12, 9, 14, 10, 12, 12, 16, 9, 16, 10, 15, 13, 16, 14, 17, 12, 20, 15, 20, 15, 19, 20, 20, 19, 22, 20, 22, 18, 21, 21, 24, 25, 27, 19, 27, 23, 26, 23, 28, 27, 25, 23, 27, 23, 29, 31

Offset: 11

Author

Michel Lagneau, Dec 23 2011

Keywords

• nonn
• base

Comments

(sum of digits of n!!) / 9 is an integer for n = 9 and n > 10.

Crossrefs

Cf. A120390.

Programs

Mathematica

Table[Sum[DigitCount[n!!][[i]]*i/9,{i,1,9}],{n,11,100}]

PARI

a(n)=my(v=eval(Vec(Str(prod(k=1,n\2,2*k+n%2)))));sum(i=1,#v,v[i])/9 \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = A120390(n)/9 for n > 10.

a(n) << n log n. Presumably a(n) ~ n log n but proving this requires showing that not too many digits are 0. (The trailing 0's in even terms are not a problem, being only about n/8.) The expected constant is 1 / (4 log 10) = 0.10857.... [Charles R Greathouse IV, Dec 23 2011]

Extensions

a(37), a(41), a(45), a(46) corrected by Georg Fischer, Jul 15 2024