

A154771


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


5



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, 34, 36, 38, 40, 33, 35, 37, 36, 41, 43, 45, 47, 49, 51, 44, 46, 48, 50, 48, 54, 56, 58, 60, 62, 55, 57, 59, 61, 63, 60, 67, 69, 71, 73, 66, 68, 70, 72, 74, 76, 72, 80, 82, 84, 77, 79, 81
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OFFSET

0,3


COMMENTS

a(n) is the sum of nth row in A218978; see also A120004.  Reinhard Zumkeller, Nov 10 2012


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000


FORMULA

a(n) = n+A154781(n).
a(10^n) = A002275(n+1).


EXAMPLE

Since n=0,...,9 has a single digit, only n itself appears as substring in k, thus a(n)=n.
10 has { 0, 1, 10 } as substrings, thus a(10) = 0+1+10 = 11.
11 has { 1, 11 } as substrings, thus a(11) = 1+11 = 12.
12 has { 1, 2, 12 } as substrings, thus a(12) = 1+2+12 = 15.


PROG

(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)~ }
(Haskell)
a154771 = sum . a218978_row :: Integer > Integer
 Reinhard Zumkeller, Nov 10 2012
(Python)
def a(n):
s = str(n); L = len(s)
return sum(set(int(s[i:j]) for i in range(L) for j in range(i+1, L+1)))
print([a(n) for n in range(73)]) # Michael S. Branicky, Nov 08 2022


CROSSREFS

Cf. A154770, A154781.
Sequence in context: A128870 A355620 A256476 * A071249 A084433 A084434
Adjacent sequences: A154768 A154769 A154770 * A154772 A154773 A154774


KEYWORD

base,easy,nonn,look


AUTHOR

M. F. Hasler, Jan 16 2009


STATUS

approved



