login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A096234 Base 10 "digit addition generators": a(n) = smallest m such that m + (sum of digits of m) = n, or -1 if no such m exists. 1
0, -1, 1, -1, 2, -1, 3, -1, 4, -1, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, -1, 15, 20, 16, 21, 17, 22, 18, 23, 19, 24, -1, 25, 30, 26, 31, 27, 32, 28, 33, 29, 34, -1, 35, 40, 36, 41, 37, 42, 38, 43, 39, 44, -1, 45, 50, 46, 51, 47, 52, 48, 53, 49, 54, -1, 55, 60, 56, 61, 57, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The -1 entries in this sequence correspond to A003052, the self numbers.

This sequence has several terms in common with A025804 (as long as we match -1's with 0's), the expansion of 1/((1-x^2)(1-x^4)(1-x^9)). a(25) to a(34) of that sequence match a(10) to a(19) of the present sequence.

There are 102 -1's in the first 1000 terms here and 983 -1's in the first 10000 terms. - Harvey P. Dale, Feb 22 2016

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, Preprint, 2021.

Eric Weisstein's World of Mathematics, Digit Addition Generator.

EXAMPLE

a(0) = 0 because 0 + 0 = 0

a(1) = -1 because there is no nonnegative integer that added to its digits-sum results in 1

a(29) = 19 because 19 + (1 + 9) = 29

a(30) = 24 because 24 + (2 + 4) = 30

a(31) = -1 because there is no integer that added to its digits-sum results in 31

MATHEMATICA

msodm[n_]:=Module[{m=n-9*IntegerLength[n]}, While[m+Total[ IntegerDigits[ m]] != n&&m<n, m++]; If[m+Total[IntegerDigits[m]]==n, m, -1]]; Array[ msodm, 80, 0] (* Harvey P. Dale, Feb 22 2016, updated Dec 31 2021 *)

PROG

/* PARI: Gen(n, b) returns a list of the generators of n in base b. Written by Max Alekseyev (see Alekseyev et al., 2021).

For example, Gen(101, 10) returns [91, 101]. - N. J. A. Sloane, Jan 02 2022 */

{ Gen(u, b=10) = my(d, m, k);

  if(u<0 || u==1, return([]); );

  if(u==0, return([0]); );

  d = #digits(u, b)-1;

  m = u\b^d;

  while( sumdigits(m, b) > u - m*b^d,

    m--;

    if(m==0, m=b-1; d--; );

  );

  k = u - m*b^d - sumdigits(m, b);

  vecsort( concat( apply(x->x+m*b^d, Gen(k, b)),

                   apply(x->m*b^d-1-x, Gen((b-1)*d-k-2, b)) ) );

}

CROSSREFS

Cf. A003052, A025804.

Sequence in context: A337377 A308059 A319698 * A340088 A087114 A303753

Adjacent sequences:  A096231 A096232 A096233 * A096235 A096236 A096237

KEYWORD

base,sign

AUTHOR

Alonso del Arte, Aug 09 2004

EXTENSIONS

Typo in definition corrected by Harvey P. Dale, Feb 22 2016

Edited. Escape clause value changed from 0 to -1, and a(0) = 0 added. - N. J. A. Sloane, Dec 31 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)