cp's OEIS Frontend

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

%I A348674 #29 Dec 19 2021 12:51:29
%S A348674 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,
%T A348674 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,
%U A348674 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
%N A348674 Number of distinct values that can be produced by splitting n and adding the parts.
%C A348674 Differs from A055642 first at n=120: a(120) = 4 != 3 = A055642(120).
%C A348674 The number of split positions can vary from 0 to length(n)-1.
%H A348674 Alois P. Heinz, <a href="/A348674/b348674.txt">Table of n, a(n) for n = 0..20000</a>
%F A348674 a(n) <= 2^floor(log_10(n)) = 2^A004216(n) for n>0.
%F A348674 a((10^n-1)/9) = a(A002275(n)) <= A000041(n) with equality only for n <= 23.
%F A348674 a(10^n) = a(A011557(n)) = n+1.
%e A348674 a(0) = 1: 0.
%e A348674 a(10) = 2: 1 = 1+0, 10.
%e A348674 a(100) = 3: 1 = 1+0+0, 10 = 10+0, 100.
%e A348674 a(120) = 4: 3 = 1+2+0, 12 = 12+0, 21 = 1+20, 120.
%e A348674 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}|.
%p A348674 b:= proc(s) option remember; (n-> {parse(s), seq(seq(seq(x+y,
%p A348674       y=b(s[i+1..n])), x=b(s[1..i])), i=1..n-1)})(length(s))
%p A348674     end:
%p A348674 a:= n-> nops(b(""||n)):
%p A348674 seq(a(n), n=0..120);
%Y A348674 Ordinal transform gives A349315.
%Y A348674 Where records occur: A349316.
%Y A348674 Cf. A000041, A002275, A004216, A007953, A011557, A055642, A089695.
%K A348674 nonn,base
%O A348674 0,11
%A A348674 _Alois P. Heinz_, Oct 29 2021