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A225673 Number of integers whose sum of substrings = n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

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.

EXAMPLE

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).

PROG

(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))

CROSSREFS

Cf. A071062, A007953.

Sequence in context: A289642 A249121 A289410 * A257779 A328865 A329623

Adjacent sequences:  A225670 A225671 A225672 * A225674 A225675 A225676

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved

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Last modified May 13 10:56 EDT 2021. Contains 343839 sequences. (Running on oeis4.)