

A154781


Sum of all numbers < n that appear as substring of n, written in decimal system.


2



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 2, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 3, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 4, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 5, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 6, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 7, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17
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OFFSET

0,13


COMMENTS

The condition "< n" narrows the meaning of "substring" to the strict sense, i.e. excludes n itself.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000


FORMULA

A154781(n) = A154771(n)n. A154781(10^n) = A002275(n). A154781(n)>0 <=> n>9.


EXAMPLE

Since n=0,...,9 has a single digit, only n itself appears as substring in n, thus a(n)=0.
10 has { 0, 1, 10 } as substrings, thus a(10) = 0+1 = 1.
11 has { 1, 11 } as substrings, thus a(11) = 1.
12 has { 1, 2, 12 } as substrings, thus a(12) = 1+2 = 3.


MATHEMATICA

san[n_]:=Total[Union[FromDigits/@Flatten[Table[Partition[IntegerDigits[n], i, 1], {i, IntegerLength[n]1}], 1]]]; Array[san, 90, 0] (* Harvey P. Dale, May 27 2017 *)


PROG

(PARI) A154781(n) = { local(d=#Str(n)); n=vecsort(concat(vector(d, i, vector(d, j, n%10^j)+(d&!n\=10))), NULL, 12); n*vector(#n, i, i>1)~ }


CROSSREFS

Cf. A154770, A154771.
Sequence in context: A077396 A243196 A247485 * A118716 A004177 A004721
Adjacent sequences: A154778 A154779 A154780 * A154782 A154783 A154784


KEYWORD

base,easy,nonn


AUTHOR

M. F. Hasler, Jan 16 2009


STATUS

approved



