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A064799 Sum of n-th prime number and n-th composite number.

%I A064799 #27 Mar 31 2024 10:23:19
%S A064799 6,9,13,16,21,25,31,34,39,47,51,58,63,67,72,79,86,89,97,103,106,113,
%T A064799 118,125,135,140,143,149,153,158,173,179,186,189,200,203,211,218,223,
%U A064799 230,237,241,253,256,261,264,277,291,296,299,305,313,316,327,334,341
%N A064799 Sum of n-th prime number and n-th composite number.
%D A064799 Ivan Grischenko, ivansasha(AT)mtu-net.ru, private communication.
%H A064799 Harry J. Smith, <a href="/A064799/b064799.txt">Table of n, a(n) for n = 1..1000</a>
%F A064799 a(n) = prime(n) + composite(n).
%F A064799 From _Jaroslav Krizek_, Dec 13 2009: (Start)
%F A064799 a(n) = A000040(n) + A002808(n).
%F A064799 a(n) = A171639(n+1). (End)
%e A064799 a(1)=6 because the first prime is 2 and the first composite is 4; 2 + 4 = 6
%e A064799 a(2)=9 because prime(2)=3 and composite(2)=6; 3 + 6 = 9.
%t A064799 Module[{nn=100,cmps},cmps=Select[Range[nn],CompositeQ];Total/@Thread[{Prime[Range[ Length[ cmps]]],cmps}]] (* _Harvey P. Dale_, Mar 31 2024 *)
%o A064799 (PARI)
%o A064799 nextComp(n)= { if (!isprime(n), return(n)); return(n + 1) }
%o A064799 { p=1; c=3; for (n=1, 100, p=nextprime(p + 1); c=nextComp(c + 1); print1(p + c, ", ") ) } \\ _Harry J. Smith_, Sep 25 2009
%o A064799 (Python)
%o A064799 from sympy import prime, composite
%o A064799 def A064799(n): return prime(n)+composite(n) # _Chai Wah Wu_, Aug 30 2021
%Y A064799 Cf. A000040, A002808, A171639.
%K A064799 nonn,easy
%O A064799 1,1
%A A064799 _Konstantin Knop_, Oct 21 2001
%E A064799 More terms from Larry Reeves (larryr(AT)acm.org), Nov 12 2001
%E A064799 Offset changed from 0 to 1 by _Harry J. Smith_, Sep 25 2009