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

1,1

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

Links

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

Formula

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

Example

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

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

Crossrefs

Sequence in context: A115039 A032536 A374167 * A217834 A227877 A225867

Adjacent sequences: A115058 A115059 A115060 * A115062 A115063 A115064

Keyword

nonn,easy

Author

Lekraj Beedassy, Mar 01 2006

Extensions

Edited and extended by Stefan Steinerberger, Oct 27 2007

Status

approved