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Search: id:A154781
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| A154781 |
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Sum of all numbers < n that appear as substring of n, written in decimal system. |
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+0
2
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| 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; listen)
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OFFSET
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0,13
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COMMENT
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The condition "< n" narrows the meaning of "substring" to the strict sense, i.e. excludes n itself.
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FORMULA
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A154781(n) = A154771(n)-n. A154781(10^n) = A002275(n). A154781(n)>0 <=> n>9.
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EXAMPLE
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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.
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PROGRAM
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(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)~ }
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CROSSREFS
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Cf. A154770, A154771.
Sequence in context: A050270 A009041 A077396 this_sequence A118716 A004177 A004721
Adjacent sequences: A154778 A154779 A154780 this_sequence A154782 A154783 A154784
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KEYWORD
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base,easy,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 16 2009
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