A050237 a(n) = the smallest number m such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of m.

1, 2, 5, 12, 38, 30, 173, 165, 12259, 8803, 36735, 67263, 5296771, 32975, 1147233

Offset

0,2

Comments

First appearance of n in A122821.

Links

Table of n, a(n) for n=0..14.

Example

a(4) = 38 because there are exactly four sets of consecutive primes which have means of 38: {31,37,41,43}, {29,...,47}, {23,...,53} and {2,...,83},

Prog

(PARI) {a(n)= m=2; starting_index=1; k=starting_index; sum_of_primes=0; prime_count=0; sets=0; until( (prime(starting_index)>m) && (sets==n), if( (prime(starting_index)> m) || (sets>n), m++; sets=0; starting_index=1; k=starting_index); sum_of_primes=sum_of_primes+prime(k); prime_count++; mean=sum_of_primes/ prime_count; if(mean<m, k++, sum_of_primes=0; prime_count=0; starting_index++; k=starting_index; if(mean==m, sets++))); return(m)} \\ Rick L. Shepherd, Jun 14 2004

Crossrefs

Cf. A060863, A082431, A122821.

Sequence in context: A115277 A130221 A036782 * A050258 A051436 A054581

Adjacent sequences: A050234 A050235 A050236 * A050238 A050239 A050240

Keyword

more,nonn

Author

Naohiro Nomoto, May 08 2003

Extensions

Edited by Don Reble, Jun 17 2003

Status

approved