A230299 Define a sequence b_s by b_s(1)=s, b_s(k+1)=b_s(k)+(sum of digits of b_s(k)); a(n) is the number of steps needed for b_n to reach a term in one of b_0, b_1, b_3 or b_9, or a(n) = -1 if b_n never joins one of these four sequences.

0, 0, 0, 0, 0, 52, 0, 11, 0, 0, 51, 50, 0, 49, 10, 0, 0, 48, 0, 9, 50, 0, 49, 0, 0, 47, 48, 0, 0, 8, 0, 49, 46, 0, 47, 48, 0, 45, 0, 0, 7, 46, 7, 47, 6, 0, 45, 44, 6, 0, 46, 0, 5, 5, 0, 45, 44, 0, 43, 4, 5, 4, 0, 0, 4, 44, 4, 43, 3, 0, 0, 42, 0, 3, 3, 4, 43, 0

Offset

0,6

Comments

We conjecture that a(n) is never -1.

Links

Lars Blomberg, Table of n, a(n) for n = 0..10000

Index entries for Colombian or self numbers and related sequences

Maple

read transforms; # to get digsum
M:=2000;
# f(s) returns the sequence k->k+digsum(k) starting at s
f:=proc(s) global M; option remember; local n, k, s1;
s1:=[s]; k:=s;
for n from 1 to M do  k:=k+digsum(k);
s1:=[op(s1), k]; od: end;
# g(s) returns (x, p), where x = first number in common between
# f(s) and one of f(1), f(3), f(9) and p is the position where it occurred.
# If f(s) and all of f(1), f(3), f(9) are disjoint for M terms, returns (-1, -1)
S1:=convert(f(1), set):
S3:=convert(f(3), set):
S9:=convert(f(9), set):
g:=proc(s) global f, S1, S3, S9; local t1, p, T0, T1, T2;
T0:=f(s):
T1:=convert(T0, set);
if ((s mod 9) = 3) or ((s mod 9) = 6) then   T2:= T1 intersect S3;   t1:=min(T2);   if (t1 = infinity) then RETURN(-1, -1); else     member(t1, T0, 'p'); RETURN(t1, p-1); fi;
elif ((s mod 9) = 0) then   T2:= T1 intersect S9;   t1:=min(T2);   if (t1 = infinity) then RETURN(-1, -1); else     member(t1, T0, 'p'); RETURN(t1, p-1); fi;
else   T2:= T1 intersect S1;   t1:=min(T2);   if (t1 = infinity) then RETURN(-1, -1); else     member(t1, T0, 'p'); RETURN(t1, p-1); fi;
fi;
end;
[seq(g(n)[2], n=1..45)];

Crossrefs

Cf. A230107, A062028, A004207, A016052, A007618, A006507, A016096.

Sequence in context: A172786 A324683 A214373 * A308235 A022079 A230107

Adjacent sequences: A230296 A230297 A230298 * A230300 A230301 A230302

Keyword

nonn,base,look

Author

N. J. A. Sloane and Reinhard Zumkeller, Oct 21 2013

Extensions

Terms a(46) and beyond from Lars Blomberg, Jan 10 2018

Status

approved