A105930 Starting position of the n-th prime in the almost-natural numbers sequence A007376.

2, 3, 5, 7, 12, 16, 24, 28, 36, 48, 52, 64, 72, 76, 84, 96, 108, 112, 124, 132, 136, 148, 156, 168, 184, 193, 199, 211, 217, 229, 271, 283, 301, 307, 337, 343, 361, 379, 391, 409, 427, 433, 463, 469, 481, 487, 523, 559, 571, 577, 589, 607, 613, 643, 661, 679

Offset: 2

Author

Alexandre Wajnberg, Apr 26 2005

Keywords

• base
• easy
• nonn

Comments

Prime number positions in the "counting digits": write the natural numbers as an infinite sequence of digits, starting at the left. a(n) is the subscript (i.e. the position in this sequence of "counting digits") of the first digit of the n-th prime.

Examples

			a(6)=16 because the sixth prime (13) appears at the 16th (and 17th) position in the "counting digits": 123456789101112-13-141516
		

Crossrefs

Cf. A007376, A103575.

Programs

Mathematica

f[n_] := Block[{d = Floor[ Log[10, n] + 1]}, d(n - 1) - Sum[9i*10^(d - i - 1), {i, d - 1}] + 1]; Table[ f[ Prime[n]], {n, 56}] (* Robert G. Wilson v, Apr 30 2005 *)

Extensions

Edited by Robert G. Wilson v, Apr 30 2005