A115760 Slowest growing sequence of numbers having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.

3, 7, 19, 55, 139, 859, 2119, 112999, 333679, 10040119, 15363619, 548687179, 16632374359, 5733638351299, 14360489685499, 433098704482699, 44258681327079259, 5009018648920510999

Offset

1,1

Comments

Inspired by A113875 (case of prime numbers). See A113832 minimal sets of primes having the P-P-A property, A115782 primes in A115760.

Equals 2*A103828(n) + 1. - N. J. A. Sloane, Apr 28 2007. This sequence is surely infinite - see comments in A103828.

After a(4), terms are == 19 mod 60. The sequence may also be defined by "a(1)=3 and for n>1, a(n) is the smallest number of the form 4k+3, a(n)>a(n-1) such that the pairwise sums of all elements are semiprimes." - Don Reble, Aug 17 2021

Links

Table of n, a(n) for n=1..18.

Formula

a(n) == 19 (mod 60) for n>4 [consequence of mod 30 congruence of A103828(n).] - Don Reble, Aug 17 2021

Example

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

Crossrefs

Cf. A113832, A113875, A115782, A175532.

Sequence in context: A183122 A104522 A351633 * A175533 A183115 A183120

Adjacent sequences: A115757 A115758 A115759 * A115761 A115762 A115763

Keyword

more,nonn

Author

Zak Seidov, Jan 30 2006

Extensions

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

More terms from Don Reble, Aug 17 2021

Status

approved