A279035 Left-concatenate zeros to 2^(n-1) such that it has n digits. In the regular array formed by listing the found powers, a(n) is the sum of (nonzero) digits in column n.

1, 2, 4, 9, 9, 9, 8, 19, 9, 8, 17, 27, 27, 27, 28, 17, 26, 35, 45, 45, 46, 37, 25, 44, 53, 65, 42, 72, 74, 52, 70, 90, 92, 74, 53, 62, 72, 70, 93, 61, 81, 80, 89, 100, 91, 80, 91, 79, 99, 99, 99, 98, 107, 117, 118, 106, 130, 86, 123, 155, 137, 117, 118, 105, 136

Offset

1,2

Comments

After carries, this is the decimal expansion of Sum_{i>=0} 0.2^i = 1.25. For n > 2, the 10^0's digit of a(n) + the 10^1's digit of a(n+1) + ... + the 10^m's digit of a(n+m) = 9 for some finite m.

Conjecture: a(n) ~ c*n where c ~= 1.93.

Conjecture: lim_{n->infinity} a(n)/n = (9/2)*log_5(2) =

1.93804... - Jon E. Schoenfield, Dec 09 2016

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Example

1
.2
. 4
. .8
. .16
. . 32
. . .64
. . .128
. . . 256
. . . .512
. . . .1024
The sum of digits of the first column is 1. Therefore, a(1) = 1.
The sum of digits in column 4 is 8 + 1 = 9. Therefore, a(4) = 9.
With the powers of 2 listed above, we can find n up to n = 7. For n > 8, some digits from 2^m compose a(n) for m > 10.

Mathematica

f[n_, b_] := Block[{k = n}, While[k < n + Floor[ k*Log10[b]], k++]; Plus @@ Mod[ Quotient[ Table[ b^j*10^(k - j), {j, n -1, k}], 10^(k - n +1)], 10]]; Table[f[n, 2], {n, 65}]
 (* Robert G. Wilson v, Dec 03 2016 *)

Crossrefs

Cf. A000079, A016134.

Sequence in context: A198679 A244285 A111422 * A076661 A258710 A246515

Adjacent sequences: A279032 A279033 A279034 * A279036 A279037 A279038

Keyword

nonn,base

Author

David A. Corneth, Dec 03 2016

Status

approved