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%I #19 Jun 21 2019 09:54:43
%S 4,6,9,13,18,22,27,31,38,45,50,58,63,67,74,83,90,95,103,108,113,121,
%T 128,138,148,153,157,162,166,177,193,200,207,214,225,230,239,247,254,
%U 263,270,277,288,292,297,305,323,337,342,346,353,360,367
%N a(n) = prime(n) + (1 + prime(1 + n))/2.
%C Primes occur at n = {4, 8, 14, 16, 19, 21, 27, 31, 37, 40, 42, 48, 51, 53, ...}: {13, 31, 67, 83, 103, 113, 157, 193, 239, 263, 277, 337, 353, 367, 389, 463, 563, 571, ...}.
%C Squares occur at n = {1, 3, 22, 35, 109, 136, 908, 936, ...}: {4, 9, 121, 225, 900, 1156, 10609, 11025, ...}.
%C Semiprimes: 4, 6, 9, 22, 38, 58, 74, 95, 121, 166, ...
%C Other interesting terms(?).
%H Robert Israel, <a href="/A283623/b283623.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 2 + (1 + 3)/2 = 4,
%e a(2) = 3 + (1 + 5)/2 = 6,
%e a(3) = 5 + (1 + 7)/2 = 9.
%p Primes:= [seq(ithprime(i),i=1..101)]:
%p map(`+`,Primes[1..-2] + Primes[2..-1]/2,1/2); # _Robert Israel_, Jun 20 2019
%t Table[Prime[k] + (1 + Prime[1 + k])/2, {k, 120}]
%o (PARI) for(n=1, 53, print1(prime(n) + (1 + prime(1 + n))/2, ", ")) \\ _Indranil Ghosh_, Mar 12 2017
%Y Cf. A000040 (primes).
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 12 2017