A261175 Number of digits of Hyperfactorial(n).

1, 1, 1, 3, 5, 8, 13, 19, 26, 35, 45, 56, 69, 84, 100, 117, 137, 158, 180, 204, 231, 258, 288, 319, 352, 387, 424, 463, 503, 546, 590, 636, 684, 734, 786, 840, 897, 955, 1015, 1077, 1141, 1207, 1275, 1345, 1418, 1492, 1568, 1647, 1728, 1811, 1896, 1983, 2072, 2163, 2257, 2352

Offset: 0

Author

Robert G. Wilson v, Aug 20 2015

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002109, A061010, A260262.

Programs

Mathematica

Table[1 + Floor@ Log10@ Hyperfactorial@ n, {n, 0, 55}]

PARI

a(n)=my(r=1);for(i=1,n+1,r *= i^i);floor(log(r)/log(10))+1 \\ Anders Hellström, Aug 20 2015

PARI

vector(60, n, n--; #Str(prod(k=2, n, k^k))) \\ Michel Marcus, Aug 20 2015

Python

A261175_list, n = [], 1
for i in range(100):
    n *= i**i
    A261175_list.append(len(str(n)))  # Chai Wah Wu, Aug 21 2015

Formula

a(n) = 1 + floor( log_10( A002109(n))) = A055642(A002109(n)).