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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 15 14:28 EDT 2019. Contains 327078 sequences. (Running on oeis4.)