A175532 -id:A175532 - cp's OEIS frontend

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

Zak Seidov, Jan 30 2006

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

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

Cf. A113832, A113875, A115782, A175532.

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

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

More terms from Don Reble, Aug 17 2021

A175533 Duplicate of A115760.

Original entry on oeis.org

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

Offset: 1

Zak Seidov, Jun 12 2010

dead

Or, for i <> j, (a(i) + a(j))/2 are primes.
From a(5)=139 onward, all terms are 19 (mod 20).
Is sequence finite?
Is this a duplicate of A115760? - R. J. Mathar, Jul 22 2010
Yes, the terms are all 3 (mod 4), just as A175533. - Don Reble, Aug 17 2021

Cf. A115760, A175532.

More terms from Don Reble, Aug 17 2021

cp's OEIS Frontend

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

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