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 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 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) \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

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