A224752 a(1)=1; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).

1, 10, 99, 899, 8099, 72898, 656088, 5904797, 53143178, 478288606, 4304597458, 38741377125, 348672394128, 3138051547155, 28242463924397, 254182175319575, 2287639577876177, 20588756200885595, 185298805807970356, 1667689252271733205, 15009203270445598846, 135082829434010389615

Offset

1,2

Comments

The sequence is infinite: a(n) always exists.

One could start with a(0) = 0, followed by the given a(n). - M. F. Hasler, Oct 10 2019

References

Eric Angelini, Postings to the Sequence Fans Mailing List, Apr 13 2013

Links

Table of n, a(n) for n=1..22.

Eric Angelini, Magic Sums

E. Angelini, Magic Sums [Cached copy, with permission]

Example

1+10=11  < 1+1 >
10+99=109  < 10+9 >
99+899=998  < 99+8 >
899+8099=8998  < 899+9 >
8099+72898=80997  < 8099+7 >
...

Mathematica

leadingDigit[x_] := IntegerPart[N[x/10^IntegerPart[Log[10, x]]]];
successor[x_] :=(
   y = 1;
   If[leadingDigit[z = 9x+y] == y, z,
      y = leadingDigit[9x];
      If[leadingDigit[z = 9x+y] == y, z,
         y += 1;
         If[leadingDigit[z = 9x+y] == y, z,
            Print["Bug"]]]]);
(* Gilles Esposito-Farèse, Apr 21 2013 *)

Prog

(PHP) <?
/*
calcul de la suite telle que la somme
s(n) + s(n+1) s'obtient en concaténant le
premier chiffre de s(n+1) après s(n).
Eric Angelini, 18/04/2013
*/
function leading_digit ($n) {
  return (int) substr("$n", 0, 1) ;
}
function successor ($n) {
  $p = 9*$n ;
  for ( $a = 1 ; $a <= 9 ; $a++ ) {
    if (leading_digit($p+$a) == $a) {
      return ($p+$a) ;
    }
  }
  die("nothing found for successor($n)") ;
}
$x = $_REQUEST["x"] ;
$n = $_REQUEST["n"] ;
if ( $n === "0" ) {
  for ($i=1 ; $i<=$x ; $i++) {
    echo "$i &rarr; ", successor($i), "<br>\n" ;
  }
} else {
  if (! $x) $x = 1 ;
  if (! $n) $n = 15 ;
  while ($n--) {
    echo "$x, " ;
    $x = successor($x) ;
  }
}
/* Eric Angelini, Apr 21 2013 */
?>
From M. F. Hasler, Oct 10 2019: (Start)
(PARI) A224752_vec(N=30)=vector(N, n, N=A224752_nxt((n>1)*N))
A224752_nxt(x, n=0)={x*=9; while(digits(x++)[1]!=n++, ); x} \\ (End)

Crossrefs

Cf. A224752-A224761.

Sequence in context: A278672 A129542 A359482 * A224761 A171315 A370043

Adjacent sequences: A224749 A224750 A224751 * A224753 A224754 A224755

Keyword

nonn,base

Author

N. J. A. Sloane, Apr 21 2013

Status

approved