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A115760
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Slowest growing sequence of numbers having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
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8
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3, 7, 19, 55, 139, 859, 2119, 112999, 333679, 10040119, 15363619, 548687179, 16632374359, 5733638351299, 14360489685499, 433098704482699, 44258681327079259, 5009018648920510999
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) == 19 (mod 60) for n>4 [consequence of mod 30 congruence of A103828(n).] - Don Reble, Aug 17 2021
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EXAMPLE
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The pairwise averages of {3,7,19} are the primes {5,11,13}.
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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