A179620 a(n) = largest k such that A002808(n+1) = A002808(n) + (A002808(n) mod k), or 0 if no such k exists.

0, 4, 7, 8, 8, 10, 13, 14, 14, 16, 19, 20, 20, 23, 24, 25, 26, 26, 28, 31, 32, 33, 34, 34, 37, 38, 38, 40, 43, 44, 44, 47, 48, 49, 50, 50, 53, 54, 55, 56, 56, 58, 61, 62, 63, 64, 64, 67, 68, 68, 70, 73, 74, 75, 76, 76, 79, 80, 80, 83, 84, 85, 86, 86, 89

Offset: 1

Author

Rémi Eismann, Jan 09 2011

Keywords

• nonn
• easy

Comments

a(n) = A002808(n) - A073783(n) if A002808(n) - A073783(n) > A073783(n), 0 otherwise.

A002808(n): composite numbers; A073783(n): first difference of composite numbers.

Examples

			For n = 1 we have A002808(n) = 4, A002808(n+1) = 6; there is no k such that 6 - 4 = 2 = (4 mod k), hence a(1) = 0.
For n = 3 we have A002808(n) = 8, A002808(n+1) = 9; 7 is the largest k such that 9 - 8 = 1 = (8 mod k), hence a(3) = 7; a(3) = A002808(3) - A073783(3) = 8 - 1 = 7.
For n = 24 we have A002808(n) = 36, A002808(n+1) = 38; 34 is the largest k such that 38 - 36 = 2 = (36 mod k), hence a(24) = 34; a(24) = A002808(24) - A073783(24) = 34.
		

Links

• Rémi Eismann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A073783, A130882, A179621, A118534, A117078, A117563, A001223.