OFFSET
1,2
COMMENTS
Conjecture from Daniel Starodubtsev and Dmitry Petukhov, Nov 19 2019: (Start)
a(8) = 20000000000000046;
a(9) = 8900000000000000000000127. (End)
EXAMPLE
a(4) = 204, because 204 = f(179) = f(185) = f(191) = f(201), which has more solutions than any smaller number.
MATHEMATICA
T = 0*Range[10^5]; f[n_] := Block[{x=n, s=n}, While[x >= 10, x = Plus@@ IntegerDigits[x]; s += x]; s]; Do[v = f[i]; If[v <= 10^5, T[[v]]++], {i, 10^5}]; Flatten[Position[T, #, 1, 1] & /@ Range[6]] (* Giovanni Resta, Jul 30 2019 *)
PROG
(PARI) f(n) = {s=n; m=n; while(sumdigits(s)>9, s=sumdigits(s); m+=s); if(n<10, m=0); m+sumdigits(s); }
g(n) = sum(k=1, n, f(k)==n);
lista(NN) = {x=1; print1(1); for(n=2, NN, if(g(n)>x, x=g(n); print1(", ", n)))} \\ Jinyuan Wang, Jul 31 2019
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Daniel Starodubtsev, Jul 28 2019
EXTENSIONS
a(7) from Bert Dobbelaere, Aug 15 2019
STATUS
approved