A113875 Slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.

3, 7, 19, 139, 859, 8179, 173059, 1026199, 1827139, 15828679, 13187242759, 18732483199, 912492556939

Offset

1,1

Comments

Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.

Links

Table of n, a(n) for n=1..13.

Andrew Granville, Prime number patterns

Formula

a(n) = 2*A119751(n)+1. - Don Reble, Aug 17 2021

Example

The pairwise averages of {3,7,19} are the primes {5,11,13}.

Mathematica

s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s

Crossrefs

Cf. A113832, A115760, A119751.

Sequence in context: A128024 A245723 A118128 * A111974 A243100 A173400

Adjacent sequences: A113872 A113873 A113874 * A113876 A113877 A113878

Keyword

nonn,hard,more

Author

T. D. Noe, Jan 26 2006

Extensions

More terms from Don Reble and Giovanni Resta, Feb 15 2006

Status

approved