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%I #15 Aug 23 2021 05:22:16
%S 3,7,19,55,139,859,2119,112999,333679,10040119,15363619,548687179,
%T 16632374359,5733638351299,14360489685499,433098704482699,
%U 44258681327079259,5009018648920510999
%N Slowest growing sequence of numbers having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
%C Inspired by A113875 (case of prime numbers). See A113832 minimal sets of primes having the P-P-A property, A115782 primes in A115760.
%C Equals 2*A103828(n) + 1. - _N. J. A. Sloane_, Apr 28 2007. This sequence is surely infinite - see comments in A103828.
%C 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
%F a(n) == 19 (mod 60) for n>4 [consequence of mod 30 congruence of A103828(n).] - _Don Reble_, Aug 17 2021
%e The pairwise averages of {3,7,19} are the primes {5,11,13}.
%Y Cf. A113832, A113875, A115782, A175532.
%K more,nonn
%O 1,1
%A _Zak Seidov_, Jan 30 2006
%E More terms from _Don Reble_ and _Giovanni Resta_, Feb 15 2006
%E More terms from _Don Reble_, Aug 17 2021
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