A096696 Consider the n-th prime, p_n, as the beginning of 2k+1 consecutive primes; then a(n) = p_(n+k) a balanced prime of order k, k maximized, or 0 if no such prime exists.

0, 5, 29, 37, 0, 0, 0, 0, 0, 149, 53, 0, 53, 71, 137, 227, 0, 0, 89, 79, 0, 0, 0, 0, 179, 0, 0, 173, 173, 0, 0, 419, 0, 157, 0, 157, 173, 0, 173, 0, 263, 0, 0, 0, 0, 211, 229, 0, 353, 397, 0, 0, 353, 359, 409, 577, 0, 353, 383, 353, 0, 0, 0, 0, 0, 0, 349, 349, 0, 0, 0, 397, 373

Offset

1,2

Comments

a(n) either equals 0 or belongs to A090403.

Links

Table of n, a(n) for n=1..73.

Example

a(2) = 5 because beginning with the second prime, 3, there is a run of three prime, (3,5,7) the average and median of which is 5.
a(5) = 0 because there does not exist a run of 2k + 1 primes such that the arithmetic mean and the median are the same.

Mathematica

f[n_] := Block[{k = 1, p = 0}, While[k < 10^4, If[(Plus @@ Table[Prime[i], {i, n, n + 2k}]) == (2k + 1)Prime[n + k], p = Prime[n + k]]; k++ ]; p]; Table[ f[n], {n, 74}]

Crossrefs

Cf. A090403.

Sequence in context: A321701 A243012 A053244 * A115279 A279393 A182288

Adjacent sequences: A096693 A096694 A096695 * A096697 A096698 A096699

Keyword

nonn

Author

Robert G. Wilson v, Jul 02 2004

Status

approved