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`%I #11 Oct 20 2020 10:00:14
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`%S 47,73,157,167,179,263,467,719,733,757,877,887,1021,1327,1367,1453,
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`%T 1613,1997,2027,2477,2593,2633,2767,2879,3001,3083,3119,3203,3307,
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`%U 3583,3623,3733,3779,4021,4157,4217,4273,4327,4561,4703,4787,4801,4933,5087,5153,5387,5399,5573,5701,5879,6343,6359
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`%N a(n) is the sum of A338270(n) and the average of the primes immediately before and after A338270(n).
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`%C All terms are prime.
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`%H Robert Israel, <a href="/A338273/b338273.txt">Table of n, a(n) for n = 1..10000</a>
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`%F a(n) = A338270(n) + (A151799(A338270(n))+A151800(A338270(n)))/2.
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`%e A338270(3) = 79 with previous and next primes 73 and 83, so a(3) = 79 + (83+83)/2 = 157.
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`%p q:= 3: r:= 5:
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`%p count:= 0: R:= NULL:
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`%p while count < 100 do
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`%p p:= q; q:= r; r:= nextprime(r);
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`%p if isprime((p+2*q+r)/2) then count:=count+1; R:= R, p + (q+r)/2;
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`%p fi
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`%p od:
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`%p R;
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`%Y Cf. A151799, A151800, A338270.
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`%K nonn
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`%O 1,1
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`%A _J. M. Bergot_ and _Robert Israel_, Oct 19 2020
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