A348674 Number of distinct values that can be produced by splitting n and adding the parts.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4

Offset

0,11

Comments

Differs from A055642 first at n=120: a(120) = 4 != 3 = A055642(120).

The number of split positions can vary from 0 to length(n)-1.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Formula

a(n) <= 2^floor(log_10(n)) = 2^A004216(n) for n>0.

a((10^n-1)/9) = a(A002275(n)) <= A000041(n) with equality only for n <= 23.

a(10^n) = a(A011557(n)) = n+1.

Example

a(0) = 1: 0.
a(10) = 2: 1 = 1+0, 10.
a(100) = 3: 1 = 1+0+0, 10 = 10+0, 100.
a(120) = 4: 3 = 1+2+0, 12 = 12+0, 21 = 1+20, 120.
a(2493690) = 62 = |{33, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 213, 267, 294, 321, 348, 375, 384, 402, 420, 510, 564, 591, 618, 708, 726, 744, 789, 807, 942, 951, 969, 1032, 1050, 1185, 2508, 2562, 2589, 3183, 3705, 3723, 3741, 3939, 4947, 5028, 9375, 9393, 24945, 25026, 49371, 93696, 93714, 249369, 493692, 2493690}|.

Maple

b:= proc(s) option remember; (n-> {parse(s), seq(seq(seq(x+y,
      y=b(s[i+1..n])), x=b(s[1..i])), i=1..n-1)})(length(s))
    end:
a:= n-> nops(b(""||n)):
seq(a(n), n=0..120);

Crossrefs

Ordinal transform gives A349315.

Where records occur: A349316.

Cf. A000041, A002275, A004216, A007953, A011557, A055642, A089695.

Sequence in context: A262190 A004218 A055642 * A276502 A138902 A211668

Adjacent sequences: A348671 A348672 A348673 * A348675 A348676 A348677

Keyword

nonn,base

Author

Alois P. Heinz, Oct 29 2021

Status

approved