A178544 a(n) are such that n or one of its substrings is divisible by every integer from 1 to a(n).

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 3, 1, 4, 1, 4, 1, 4, 1, 4, 1, 2, 2, 4, 4, 2, 5, 4, 2, 4, 4, 2, 1, 2, 1, 6, 1, 8, 1, 2, 1, 6, 3, 3, 3, 4, 3, 3, 3, 4, 3, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 4, 2, 4, 4, 2, 4, 4, 2, 4, 3, 1, 4, 1, 4, 1, 4, 1, 4, 1, 2, 2, 3, 3, 2, 3

Offset: 1

Author

Zak Seidov, May 29 2010

Keywords

• base
• nonn

Comments

Positions of records 1,2,6,12,45,54,56,... are terms in A177834 (with repetitions).

Examples

			a(56)=8 because divisors of 56 are d1={1,2,4,7,8,14,28,56},
divisors of 5 are d2={1, 5}, divisors of 6 are d3={1,2,3,6},
and union of d1, d2, d3 gives 8 subsequent integers 1..8 (14,28,.. not counted).
		

Crossrefs

A177834.

Programs

Mathematica

Table[id=IntegerDigits[n]; FLA=Flatten[Table[Partition[id, k, 1],
{k,Length[id]}], 1]; fd = Complement[Union[FromDigits /@ FLA], {0}];
dv=Union[Flatten[Divisors /@ fd]]; Complement[Range[100], dv][[1]]-1, {n,10^3}]