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%I #17 Nov 08 2022 13:58:40
%S 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,
%T 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,
%U 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
%N Sum of all numbers < n that appear as substring of n, written in decimal system.
%C The condition "< n" narrows the meaning of "substring" to the strict sense, i.e., excludes n itself.
%H Harvey P. Dale, <a href="/A154781/b154781.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A154771(n)-n. a(10^n) = A002275(n). a(n)>0 <=> n>9.
%e Since n=0,...,9 has a single digit, only n itself appears as substring in n, thus a(n)=0.
%e 10 has { 0, 1, 10 } as substrings, thus a(10) = 0+1 = 1.
%e 11 has { 1, 11 } as substrings, thus a(11) = 1.
%e 12 has { 1, 2, 12 } as substrings, thus a(12) = 1+2 = 3.
%t 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 *)
%o (PARI) A154781(n) = { local(d=#Str(n)); n=vecsort(concat(vector(d,i,vector(d,j,n%10^j)+(d--&!n\=10))),,12);n*vector(#n,i,i>1)~ }
%o (Python)
%o def a(n):
%o s = str(n)
%o return sum(set(int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))) - n
%o print([a(n) for n in range(90)]) # _Michael S. Branicky_, Nov 08 2022
%Y Cf. A154770, A154771.
%K base,easy,nonn
%O 0,13
%A _M. F. Hasler_, Jan 16 2009
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