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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 22 22:02 EDT 2023. Contains 361434 sequences. (Running on oeis4.)