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

0,12

Links

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

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]

Example

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.

Mathematica

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

Crossrefs

Cf. A093882.

Sequence in context: A103693 A117230 A093882 * A307629 A053392 A114925

Adjacent sequences: A138950 A138951 A138952 * A138954 A138955 A138956

Keyword

nonn,base

Author

Zak Seidov, Apr 04 2008

Status

approved