A007618 -id:A007618 - cp's OEIS frontend

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

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

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

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

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)];

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

A249043 a(1) = 42; a(n+1) = a(n) + sum of decimal digits of a(n).

Original entry on oeis.org

42, 48, 60, 66, 78, 93, 105, 111, 114, 120, 123, 129, 141, 147, 159, 174, 186, 201, 204, 210, 213, 219, 231, 237, 249, 264, 276, 291, 303, 309, 321, 327, 339, 354, 366, 381, 393, 408, 420, 426, 438, 453, 465, 480, 492, 507, 519, 534, 546, 561, 573, 588, 609, 624, 636

Offset: 1

N. J. A. Sloane, Oct 30 2014

D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
Index entries for Colombian or self numbers and related sequences

Cf. A004207, A016052, A007618, A006507, A016052, A036228.

Cf. A007953, A062028.

a249043 n = a249043_list !! (n-1)
a249043_list = iterate a062028 42
-- Reinhard Zumkeller, Oct 31 2014

a(n+1) = A062028(a(n)). - Reinhard Zumkeller, Oct 31 2014

A292202 The n-th iteration of A062028 starting with n.

Original entry on oeis.org

2, 8, 15, 28, 25, 33, 59, 77, 90, 79, 109, 111, 134, 137, 129, 148, 184, 189, 218, 197, 204, 226, 250, 231, 284, 284, 297, 313, 325, 309, 341, 398, 354, 418, 418, 414, 488, 440, 438, 478, 529, 465, 545, 554, 531, 628, 658, 561, 620, 677, 624, 697, 697, 657, 785, 818, 735, 865, 835, 762, 851, 851

Offset: 1

Peter Weiss, Sep 11 2017

a(n) == n*2^n (mod 9). This has a period of 18. - Robert Israel, Sep 11 2017

			n=5: 5+5=10, 10+1+0=11, 11+1+1=13, 13+1+3=17, 17+1+7=25. After 5 iterations you get 25, so a(5)=25.

Robert Israel, Table of n, a(n) for n = 1..10000
Robert Israel, Plot of a(n)/n for n = 1 .. 4000

Cf. A007618, A006507, A062028, A016096.

A062028:= proc(t) option remember; t + convert(convert(t,base,10),`+`):end proc:
seq((A062028@@n)(n), n=1..100); # Robert Israel, Sep 11 2017

Table[Nest[# + Total@ IntegerDigits@ # &, n, n], {n, 62}] (* Michael De Vlieger, Sep 11 2017 *)

a(n) = my(x=n); for (k=1, n, x += sumdigits(x)); x; \\ Michel Marcus, Sep 12 2017

A036227 a(1) = 20; a(n+1) = a(n) + sum of decimal digits of a(n).

Original entry on oeis.org

20, 22, 26, 34, 41, 46, 56, 67, 80, 88, 104, 109, 119, 130, 134, 142, 149, 163, 173, 184, 197, 214, 221, 226, 236, 247, 260, 268, 284, 298, 317, 328, 341, 349, 365, 379, 398, 418, 431, 439, 455, 469, 488, 508, 521, 529, 545, 559, 578, 598, 620, 628, 644, 658

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

elements >= 109 can be found in A007618.

Index entries for Colombian or self numbers and related sequences

Cf. A004207, A016052, A007618, A006507, A016052.

NestList[#+Total[IntegerDigits[#]]&,20,60] (* Harvey P. Dale, May 11 2014 *)

Edited by Charles R Greathouse IV, Aug 02 2010

A036233 Inverse Colombian function.

Original entry on oeis.org

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 5, 7, 3, 1, 5, 9, 7, 20, 3, 20, 1, 3, 5, 20, 9, 1, 7, 3, 31, 5, 3, 20, 31, 9, 5, 1, 3, 7, 20, 42, 31, 7, 9, 20, 5, 42, 1, 31, 3, 7, 53, 9, 31, 20, 3, 5, 7, 42, 53, 1, 9, 64, 31, 42, 20, 53, 3, 1, 5, 9, 7, 64, 75, 31, 1, 42, 5, 20, 9, 53, 7, 3, 64, 86, 75, 20

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

a(n) is the smallest x with n in the digit summing sequence starting with x.

Contains only self-numbers, see A003052.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Sean A. Irvine, Java program (github)

Cf. A004207, A016052, A007618, A006507, A016052.

A151942 Table of Self / Colombian numbers and their descendents.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 8, 12, 10, 7, 16, 15, 11, 14, 9, 23, 21, 13, 19, 18, 20, 28, 24, 17, 29, 27, 22, 31, 38, 30, 25, 40, 36, 26, 35, 42, 49, 33, 32, 44, 45, 34, 43, 48, 53, 62, 39, 37, 52, 54, 41, 50, 60, 61, 64, 70, 51, 47, 59, 63, 46, 55, 66, 68, 74, 75, 77, 57, 58, 73, 72, 56

Offset: 1

Carl R. White, Jul 13 2009

Initially resembles a permutation of the integers, but this is not the case. 101 is the first number to appear twice, descending from both 91 and 100: 91 + 9+1 = 100 + 1+0+0 = 101

D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]
Index entries for Colombian or self numbers and related sequences

First column of table is the Self numbers: A003052; First through eighth rows are A004207, A016052, A007618, A006507, A016096, A036227, A036228 respectively.

T(r,0) are those numbers not of form n + sum of digits of n (Self numbers)

T(r,c) = T(r,c-1) + sum of digits of T(r,c-1)

A292512 Sequence A: Start with n, add the sum of digits of n (A062028) and repeat. Sequence B: Start with n, add the sum of base-100 digits of n and repeat. a(n) is the smallest common number > n.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 221, 341, 24, 109, 218, 30, 1171, 173, 36, 406, 80, 84, 88, 851, 96, 163, 104, 54, 218, 346, 120, 628, 1171, 231, 173, 181, 72, 197, 406, 213, 538, 260, 237, 1003, 1705, 90, 184, 719, 1041, 1015, 365, 111, 320, 127, 117, 418, 488, 114, 1487, 137, 120, 122, 199, 126, 1171, 298, 231, 134, 677

Offset: 1

Peter Weiss, Sep 18 2017

If you start with n=1 and take a third sequence C (n + sum of base-1000 digits of n), the first common numbers of the three sequences are 2, 4, 8, 16 and 1027975.
The common numbers for the first ten primes are:
                    2 -> 4, 8, 16, 1027975, ...
                    3 -> 24, 96, 60342, ...
                    5 -> 10, 469534, ...
                    7 -> 14, 131558, ...
                   11 -> 923428, ...
                   13 -> 668495, ...
                   17 -> 81820, ...
                   19 -> 2061797, ...
                   23 -> 2227118, ...
                   29 -> 12278, ...

			n=10: Sequence A: 10, 11, 13, 17, 25, 32, 37, 47, 58, 71, 79, 95, 109, 119, 130, 134, 142, 149, 163, 173, 184, 197, 214, 221, ...
Sequence B: 10, 20, 40, 80, 160, 221, ...
-> 221 is the first common number > 10, so a(n)=221.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A286660, A062028, A007618, A006507, A016096.

With[{m = 10^3}, Table[With[{A = Rest@ NestList[# + Total@ IntegerDigits@ # &, n, m]}, NestWhile[# + Total@ IntegerDigits[#, 100] &, n, FreeQ[A, #] &, 1, m]], {n, 68}]] (* Michael De Vlieger, Sep 23 2017 *)

a(n) = my (A=n + sumdigits(n), B=n + sumdigits(n,100)); while (1, if (A==B, return (A), ARémy Sigrist, Sep 23 2017

A036230 a(n+1) = a(n) + sum of digits of a(n) starting with 110.

Original entry on oeis.org

110, 112, 116, 124, 131, 136, 146, 157, 170, 178, 194, 208, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538, 554, 568, 587, 607, 620, 628, 644, 658, 677, 697, 719

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

Elements >= 218 can be found in A004207.

Cf. A004207, A016052, A007618, A006507, A016052.

NestList[#+Total[IntegerDigits[#]]&,110,50] (* Harvey P. Dale, Oct 01 2017 *)

A036231 a(n+1) = a(n) + sum of digits of a(n) starting with 121.

Original entry on oeis.org

121, 125, 133, 140, 145, 155, 166, 179, 196, 212, 217, 227, 238, 251, 259, 275, 289, 308, 319, 332, 340, 347, 361, 371, 382, 395, 412, 419, 433, 443, 454, 467, 484, 500, 505, 515, 526, 539, 556, 572, 586, 605, 616, 629, 646, 662, 676, 695, 715, 728, 745

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

Elements >= 1003 can be found in A004207.

Cf. A004207, A016052, A007618, A006507, A016052.

A036232 a(n+1) = a(n) + sum of digits of a(n) starting with 211.

Original entry on oeis.org

211, 215, 223, 230, 235, 245, 256, 269, 286, 302, 307, 317, 328, 341, 349, 365, 379, 398, 418, 431, 439, 455, 469, 488, 508, 521, 529, 545, 559, 578, 598, 620, 628, 644, 658, 677, 697, 719, 736, 752, 766, 785, 805, 818, 835, 851, 865, 884, 904, 917, 934

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

Elements >= 317 can be found in A007618.

Cf. A004207, A016052, A007618, A006507, A016052.

NestList[#+Total[IntegerDigits[#]]&,211,50] (* Harvey P. Dale, Jul 16 2020 *)

cp's OEIS Frontend

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.

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A249043 a(1) = 42; a(n+1) = a(n) + sum of decimal digits of a(n).

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A292202 The n-th iteration of A062028 starting with n.

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A036227 a(1) = 20; a(n+1) = a(n) + sum of decimal digits of a(n).

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A036233 Inverse Colombian function.

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A151942 Table of Self / Colombian numbers and their descendents.

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A292512 Sequence A: Start with n, add the sum of digits of n (A062028) and repeat. Sequence B: Start with n, add the sum of base-100 digits of n and repeat. a(n) is the smallest common number > n.

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A036230 a(n+1) = a(n) + sum of digits of a(n) starting with 110.

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A036231 a(n+1) = a(n) + sum of digits of a(n) starting with 121.

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