A198036 Number of iterations of k = digitsum(n*k) until a number appears twice, starting with k = 1.

2, 7, 4, 5, 7, 4, 5, 4, 3, 2, 8, 4, 5, 8, 4, 5, 4, 3, 3, 7, 5, 5, 8, 4, 5, 4, 3, 3, 8, 4, 5, 8, 4, 5, 4, 3, 3, 8, 5, 5, 8, 5, 5, 4, 3, 3, 9, 4, 5, 7, 5, 8, 4, 4, 3, 8, 5, 8, 9, 4, 8, 6, 4, 3, 8, 4, 5, 8, 4, 5, 6, 4, 3, 8, 5, 5, 8, 4

Offset

1,1

Comments

Take n, then starting with k=1, apply iteration k = digitsum(n*k), stop when the new k appears before in the row, length of the n-th row is a(n):

n=1: {1,1}, a(1)=2

n=2: {1,2,4,8,7,5,1}, a(2)=7

n=3: {1,3,9,9}, a(3)=4

n=4: {1,4,7,10,4}, a(4)=5.

Links

Table of n, a(n) for n=1..78.

Mathematica

Table[k = 1; s = {k}; While[k = Total[IntegerDigits[n*k]]; FreeQ[s, k], AppendTo[s, k]]; Length[s] + 1, {n, 100}]

Crossrefs

Sequence in context: A222237 A347767 A325644 * A316249 A197143 A132724

Adjacent sequences: A198033 A198034 A198035 * A198037 A198038 A198039

Keyword

nonn,base

Author

Zak Seidov, Oct 20 2011

Status

approved