A088800 Numbers n which are divisors of the number formed by concatenating (n-1), (n-2), (n-3) and (n-4) in that order.

16, 43, 86, 3923, 7846, 1320532, 14869252, 37031789, 74063578, 1770748607, 3541497214, 7082994428, 50541770557, 1040474831558, 1076026363388, 2080949663116, 2746369613531, 3376243036861, 5492739227062, 6529386313577

Offset: 1

Author

Chuck Seggelin, Oct 20 2003

Keywords

• base
• nonn

Comments

Each member of this sequence appears to also be a factor of the number formed by concatenating (n+1), (n+2), (n+3) and (n+4) in that order. When evaluating concat((n+1),(n+2),(n+3),(n+4)) - concat((n-1),(n-2),(n-3),(n-4)) for members larger than 86 the difference appears to always be a number of the form 2(0)...4(0)...6(0)...8 with the same number of zeros following the 2, 4 and 6. The member will be a factor of this number. Further terms for the sequence can be produced by factoring numbers of this form. Let z=the number of zeros in one of the segments of a number d of the form 2(0)...4(0)...6(0)...8. Find the divisors of d. All divisors which are not of length z+1 are not members of this sequence and those that are of length z+1 are likely candidates and should be tested (note that apart from 16, candidates which are divisible by 8 appear to never be members). For example let d = 2000000000000000400000000000000060000000000000008. z=15. The divisors of d are numerous, but only one is z+1 (16) digits long: 7547657634163187. Testing this candidate confirms that it is also a member of this sequence.

Examples

			a(3)=86 because 86 is a factor of 85848382.
		

Crossrefs

Cf. A069860, A088797, A088798, A088799.