Search: id:A154781
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%I A154781
%S A154781 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,
%T A154781 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,
%U A154781 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
%N A154781 Sum of all numbers < n that appear as substring of n, written in decimal 
               system.
%C A154781 The condition "< n" narrows the meaning of "substring" to the strict 
               sense, i.e. excludes n itself.
%F A154781 A154781(n) = A154771(n)-n. A154781(10^n) = A002275(n). A154781(n)>0 <=> 
               n>9.
%e A154781 Since n=0,...,9 has a single digit, only n itself appears as substring 
               in n, thus a(n)=0.
%e A154781 10 has { 0, 1, 10 } as substrings, thus a(10) = 0+1 = 1.
%e A154781 11 has { 1, 11 } as substrings, thus a(11) = 1.
%e A154781 12 has { 1, 2, 12 } as substrings, thus a(12) = 1+2 = 3.
%o A154781 (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)~ }
%Y A154781 Cf. A154770, A154771.
%Y A154781 Sequence in context: A050270 A009041 A077396 this_sequence A118716 A004177 
               A004721
%Y A154781 Adjacent sequences: A154778 A154779 A154780 this_sequence A154782 A154783 
               A154784
%K A154781 base,easy,nonn
%O A154781 0,13
%A A154781 M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 16 2009

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