A138953 - OEIS

%I #23 May 13 2013 19:04:39

%S 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,11,3,4,5,

%T 6,7,8,9,10,11,12,4,5,6,7,8,9,10,11,12,13,5,6,7,8,9,10,11,12,13,14,6,

%U 7,8,9,10,11,12,13,14,15,7,8,9,10,11,12,13,14,15,16,8,9,10,11,12,13,14,15

%N Sum of numbers from all substrings of n.

%H Zak Seidov and Christian N. K. Anderson, <a href="/A138953/b138953.txt">Table of n, a(n) for n = 0..10000</a> (first 1000 terms from Zak Seidov)

%F a(n) = A071980(n) - n. [_R. J. Mathar_, Jul 06 2009]

%F Note: Mathar's formula works for numbers with 1, 2 or 3 digits, but thereafter only for numbers whose internal digits are zeros. [_Christian N. K. Anderson_, May 13 2013]

%e One-digit numbers have no substring, hence a(0..9)=0;

%e a(10)  = 1+0 = 1,

%e a(123) = 1+2+3+12+23 = 41,

%e a(150) = 1+5+0+15+50 = 71.

%t Table[id=IntegerDigits[n]; Total[Flatten[Table[FromDigits/@ Partition[id,k,1], {k,Length[id]-1}]]], {n,0,150}]

%Y Cf. A093882.

%K nonn,base

%O 0,12

%A _Zak Seidov_, Apr 04 2008