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

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

Offset: 0

Author

M. F. Hasler, Jan 16 2009

Keywords

• base
• easy
• nonn
• look

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A154770, A154781.

Programs

Haskell

a154771 = sum . a218978_row :: Integer -> Integer
-- Reinhard Zumkeller, Nov 10 2012

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)~ }

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

Formula

a(n) = n+A154781(n).

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