A082431 a(n) = the smallest prime p such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of p.

2, 5, 89, 53, 157, 173, 1597, 15233, 8803, 106753, 1570927, 5296771

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Example

a(4) = 53 because there are exactly four sets of consecutive primes which have means of 53: {53}, {47,53,59}, {41,...,67} and {31,...,73},

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=nextprime(m+1); 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. A050221, A050237, A060863, A082370.

Sequence in context: A120798 A048187 A378088 * A023272 A057978 A093308

Adjacent sequences: A082428 A082429 A082430 * A082432 A082433 A082434

Keyword

more,nonn

Author

Naohiro Nomoto, May 11 2003

Extensions

Edited by Don Reble, Jun 17 2003

Status

approved