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

Author

Naohiro Nomoto, May 08 2003

Keywords

• more
• nonn

Comments

First appearance of n in A122821.

Examples

			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},
		

Crossrefs

Cf. A060863, A082431, A122821.

Programs

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(meanRick L. Shepherd, Jun 14 2004

Extensions

Edited by Don Reble, Jun 17 2003