A225673 Number of integers whose sum of substrings = n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 7, 7, 5, 5, 3, 3, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 3, 4, 4, 5, 4, 5, 4, 5, 3, 4, 3, 4, 4, 5, 5, 6, 5, 6, 5, 5, 4, 5, 4, 5, 5, 6, 6, 7, 6, 7, 5, 6

Offset: 1

Author

Christian N. K. Anderson and Kevin L. Schwartz, May 11 2013

Keywords

• nonn
• base

Comments

20 is the first number that is not the sum of substrings of any positive integer. There are 203 such numbers < 10000, and they disproportionately begin with 2 and 3 -- 123 of them and 70 of them, respectively.

Examples

			For a(59)=5, the five solutions are:
136 (because 13+36+1+3+6=59),
140 (because 14+40+1+4+0=59),
317 (because 31+17+3+1+7=59),
321 (because 32+21+3+2+1=59), and
502 (because 50+02+5+0+2=59).
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
• Christian N. K. Anderson, Table of n, a(n), and all integer solutions.
• Christian N. K. Anderson, Ulam Spiral of n = 1..10000, color-coded by their value in this sequence.

Crossrefs

Cf. A071062, A007953.

Programs

R

table(factor(sapply(1:900,function(n) { tot=0; s=as.character(n); len=nchar(s); for(i in 1:len) for(j in i:len) tot=tot+as.numeric(substr(s,i,j)); tot-n } ),levels=1:100))