A138953 Sum of numbers from all substrings of n.

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, 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, 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

Offset: 0

Author

Zak Seidov, Apr 04 2008

Keywords

• nonn
• base

Examples

			One-digit numbers have no substring, hence a(0..9)=0;
a(10)  = 1+0 = 1,
a(123) = 1+2+3+12+23 = 41,
a(150) = 1+5+0+15+50 = 71.
		

Links

• Zak Seidov and Christian N. K. Anderson, Table of n, a(n) for n = 0..10000 (first 1000 terms from Zak Seidov)

Crossrefs

Cf. A093882.

Programs

Mathematica

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

Formula

a(n) = A071980(n) - n. [R. J. Mathar, Jul 06 2009]

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]