A106848 a(n) = the number of times the last digit of n must be appended to n to form a number m such that n divides m, or 0 if no such m exists.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 6, 6, 3, 0, 16, 9, 18, 1, 6, 2, 22, 0, 0, 6, 27, 6, 28, 1, 15, 0, 2, 16, 6, 0, 3, 18, 6, 1, 5, 6, 21, 2, 9, 22, 46, 0, 42, 1, 48, 0, 13, 27, 2, 0, 18, 28, 58, 1, 60, 15, 6, 0, 6, 2, 33, 16, 22, 1, 35, 0, 8, 3, 0, 0, 2, 6, 13, 1, 81, 5, 41, 6, 16, 21, 84, 2, 44, 1

Offset: 1

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), May 08 2005

Keywords

• base
• nonn

Comments

Shares many terms in common with A064696, which involved inserting zeros between digits. Numbers which do not appear to be able to form a multiple (a(n)=0) were tested out to 10000 digits added. Note those values of n for which a(n)=0 (12, 16, 24, 25, 32, 36, 48, ...) appear to be given by A064695.

Examples

			a(13) = 6 because the last digit of 13 must be appended to it six times before a new number which divides 13 is formed. (I.e., 133 mod 13 = 3, 1333 mod 13 = 7, 13333 mod 13 = 8, 133333 mod 13 = 5, 1333333 mod 13 = 6, 13333333 mod 13 = 0.) a(12)=0 because no matter how many 2's are appended to 12, the resulting number is not divisible by 12.
		

Crossrefs

Cf. A106849.