A244598 Integers n such that for every k > 0, n*10^k-1 has a divisor in the set { 11, 73, 101, 137 }.

152206, 1522060, 4109489, 4459665, 6001522, 7761557, 9489041, 10948904

Offset

1,1

Comments

For n > 8, a(n) = a(n-8) + 11111111, the first 8 values are given in the data.

If n is of the form 3*m+1 then n*10^k-1 is always divisible by 3 but also has a divisor in the set { 11, 73, 101, 137 }.

If k of the form 2*j+1, n*10^(2*j+1)-1 is divisible by 11.

If k of the form 8*j, n*10^(8*j)-1 is divisible by 73.

If k of the form 4*j+2, n*10^(4*j+2))-1 is divisible by 101.

If k of the form 8*j+4 then n*10^(8*j+4)-1 is divisible by 137.

This covers all k, so the covering set is { 11, 73, 101, 137}.

Links

Table of n, a(n) for n=1..8.

Formula

For n > 8 a(n) = a(n-8) + 11111111.

Crossrefs

Cf. A243969, A243974, A244348.

Sequence in context: A205462 A248691 A086691 * A112625 A118498 A233392

Adjacent sequences: A244595 A244596 A244597 * A244599 A244600 A244601

Keyword

nonn,more

Author

Pierre CAMI, Jul 01 2014

Status

approved