cp's OEIS Frontend

A154771 Sum of all numbers that appear as substring of n, written in decimal system.

%I A154771 #17 Nov 09 2022 19:25:05
%S A154771 0,1,2,3,4,5,6,7,8,9,11,12,15,17,19,21,23,25,27,29,22,24,24,28,30,32,
%T A154771 34,36,38,40,33,35,37,36,41,43,45,47,49,51,44,46,48,50,48,54,56,58,60,
%U A154771 62,55,57,59,61,63,60,67,69,71,73,66,68,70,72,74,76,72,80,82,84,77,79,81
%N A154771 Sum of all numbers that appear as substring of n, written in decimal system.
%C A154771 a(n) is the sum of n-th row in A218978; see also A120004. - _Reinhard Zumkeller_, Nov 10 2012
%H A154771 Reinhard Zumkeller, <a href="/A154771/b154771.txt">Table of n, a(n) for n = 0..10000</a>
%F A154771 a(n) = n+A154781(n).
%F A154771 a(10^n) = A002275(n+1).
%e A154771 Since n=0,...,9 has a single digit, only n itself appears as substring in k, thus a(n)=n.
%e A154771 10 has { 0, 1, 10 } as substrings, thus a(10) = 0+1+10 = 11.
%e A154771 11 has { 1, 11 } as substrings, thus a(11) = 1+11 = 12.
%e A154771 12 has { 1, 2, 12 } as substrings, thus a(12) = 1+2+12 = 15.
%o A154771 (PARI) A154771(n) = { local(d=#Str(n)); n=vecsort(concat(vector(d,i,vector(d,j,n%10^j)+(d--&!n\=10))),,8);n*vector(#n,i,1)~ }
%o A154771 (Haskell)
%o A154771 a154771 = sum . a218978_row :: Integer -> Integer
%o A154771 -- _Reinhard Zumkeller_, Nov 10 2012
%o A154771 (Python)
%o A154771 def a(n):
%o A154771     s = str(n); L = len(s)
%o A154771     return sum(set(int(s[i:j]) for i in range(L) for j in range(i+1, L+1)))
%o A154771 print([a(n) for n in range(73)]) # _Michael S. Branicky_, Nov 08 2022
%Y A154771 Cf. A154770, A154781.
%K A154771 base,easy,nonn,look
%O A154771 0,3
%A A154771 _M. F. Hasler_, Jan 16 2009