A362680 a(n) is the number of decimal digits in A173426(n).

1, 3, 5, 7, 9, 11, 13, 15, 17, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232

Offset: 1

Author

David Cleaver, Apr 29 2023

Keywords

• nonn
• base
• easy

Examples

			a(12)=28 since 1234567891011121110987654321 has 28 digits.
		

Links

• Stefano Spezia, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A173426, A058183, A055642.

Programs

Mathematica

a[n_]:=IntegerLength[FromDigits[Flatten[IntegerDigits/@Join[Range[n], Reverse[Range[n-1]]]]]]; Array[a,63] (* Stefano Spezia, Apr 16 2025 *)

PARI

a(n)={my(t=logint(n,10)+1); 2*n*t-2*(10^t-1)/9+t}

Python

def a(n): return ((n*(t:=len(str(n)))-(10**t-1)//9)<<1) + t
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, May 02 2023

Formula

a(n) = A058183(n) + A058183(n-1), for n >= 2.

a(n) = A055642(A173426(n)).

a(n) = 2*A058183(n) - A055642(n).