login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 10
1, 10, 99, 899, 8099, 72898, 656088, 5904797, 53143178, 478288606, 4304597458, 38741377125, 348672394128, 3138051547155, 28242463924397, 254182175319575, 2287639577876177, 20588756200885595, 185298805807970356, 1667689252271733205, 15009203270445598846, 135082829434010389615 (list; graph; refs; listen; history; text; internal format)
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: A299952 A278672 A129542 * A224761 A171315 A081109

Adjacent sequences:  A224749 A224750 A224751 * A224753 A224754 A224755

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Apr 21 2013

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 19:49 EST 2020. Contains 332110 sequences. (Running on oeis4.)