A115061 a(n) is the number of occurrences of the n-th prime number in A051697.

3, 2, 2, 3, 3, 3, 3, 3, 5, 4, 4, 5, 3, 3, 5, 6, 4, 4, 5, 3, 4, 5, 5, 7, 6, 3, 3, 3, 3, 9, 9, 5, 4, 6, 6, 4, 6, 5, 5, 6, 4, 6, 6, 3, 3, 7, 12, 8, 3, 3, 5, 4, 6, 8, 6, 6, 4, 4, 5, 3, 6, 12, 9, 3, 3, 9, 10, 8, 6, 3, 5, 7, 7, 6, 5, 5, 7, 6, 6

Offset: 1

Author

Lekraj Beedassy, Mar 01 2006

Keywords

• nonn
• easy

Comments

Except for the second entry, the sequence also holds with respect to A077018.

a(n) equals A162345(n) for n>1 and equals A052288(n-2) for n>2. - Nathaniel Johnston, Jun 25 2011

Examples

			The 5th prime number, 11, appears three times in A051697. Therefore a(5) = 3.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Programs

Mathematica

a = {3}; For[n = 2, n < 100, n++, c = 0; For[j = Prime[n - 1], j < Prime[n + 1], j++, If[j < Prime[n], If[Prime[n] - j < j - Prime[n - 1], c++ ], If[Not[Prime[n + 1] - j < j - Prime[n]], c++ ]]]; AppendTo[a, c]]; a

Formula

a(n) = (prime(n+1) - prime(n-1))/2 for n>=3. - Nathaniel Johnston, Jun 25 2011

Extensions

Edited and extended by Stefan Steinerberger, Oct 27 2007