A115760 Slowest growing sequence of numbers having the prime-pairwise-average property: if i

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

Offset: 1

Author

Zak Seidov, Jan 30 2006

Keywords

• more
• nonn

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

Examples

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

Crossrefs

Cf. A113832, A113875, A115782, A175532.

Formula

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

Extensions

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

More terms from Don Reble, Aug 17 2021