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A128546 Inrepfigit (INverse REPetitive FIbonacci-like diGIT) numbers (or Htiek numbers). 2
17, 21, 25, 42, 63, 84, 143, 286, 2355, 5821, 6618, 11709, 12482, 33747, 39571, 129109, 466957, 1162248, 1565166, 1968084, 3636638, 3853951, 4898376, 6065280, 13443745, 13933175, 17118698, 22421197, 24153462377 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..29.

EXAMPLE

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

MATHEMATICA

iKeithQ[n_Integer] := Module[{b = Reverse[IntegerDigits[n]], s, k = 0}, s = Total[b]; While[s < n, AppendTo[b, s]; k++; s = 2*s - b[[k]]]; s == n]; Select[Range[10, 100000], iKeithQ] (* T. D. Noe, Mar 15 2011 *)

PROG

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;

}

CROSSREFS

Cf. A007629.

Cf. A097060 (reverse of these numbers).

Sequence in context: A039505 A166875 A282109 * A188200 A060875 A259555

Adjacent sequences:  A128543 A128544 A128545 * A128547 A128548 A128549

KEYWORD

base,nonn

AUTHOR

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

STATUS

approved

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Last modified August 22 03:23 EDT 2017. Contains 290942 sequences.