

A138953


Sum of numbers from all substrings of n.


4



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
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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

Onedigit 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



