1,1

This sequence is similar to A007629 (Keith numbers). It consists of the numbers n>9 with the following property: n is a term of the sequence S whose k first terms are the k digits of n (with the first term equal to the units digit), and with S(n+1)=sum of the k previous terms.

42 is in the sequence because the terms of the sequence it creates are 2, 4, 6, 10, 16, 26, 42, ...

Here is a (messy) C++ code which finds the terms of the sequence below 100000000

#include <stdio.h>

int main()

{

int k2;

for ( int k = 10 ; k < 100000000 ; k++ )

{

k2 = k;

int array [9];

for ( int i = 0 ; i <= 8; i++ )

{

array[i] = k2 % 10;

k2 /= 10;

}

bool c = true;

int check=8;

for ( int i = 0; i <=8; i++ )

{

if ((array[8-i]==0)&&c)

check--;

else

c=false;

}

bool b = false;

int n = 0;

while ( n <= k && !b )

{

n = 0;

for ( int i = 0; i <= check; i++ )

n += array[i];

if ( n == k )

b = true;

for ( int i = 0 ; i < check ; i++ )

array[i] = array[i+1];

array[check] = n;

}

if ( b )

printf("%d

", k);

}

return 0;

}

Cf. A007629.

Sequence in context: A140146 A039502 A039505 this_sequence A060875 A138600 A050845

Adjacent sequences: A128543 A128544 A128545 this_sequence A128547 A128548 A128549

base,nonn

Pierre Karpman (pierre.karpman(AT)laposte.net), Oct 23 2007