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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

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

LINKS

Table of n, a(n) for n=0..89.

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.

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

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Last modified March 27 22:02 EDT 2017. Contains 284182 sequences.