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%I #28 Dec 12 2021 19:35:57
%S 4,4,8,10,14,16,20,22,30,30,38,40,44,46,54,58,62,66,72,72,80,82,90,96,
%T 102,102,108,108,114,126,132,136,140,148,152,156,164,166,174,178,182,
%U 190,194,196,200,210,224,226,230,232,240,240,252,256,264,268,272,276
%N In sequence of odd primes add 1 to first prime, 3rd prime, 5th prime, ... then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.
%F a(n) = prime(n+1) + (-1)^(n+1). - _Juri-Stepan Gerasimov_, Sep 10 2009
%F a(n) = odd prime(n) - (-1)^n. - _Juri-Stepan Gerasimov_, Sep 10 2009
%F a(n) + a(n-1) = prime(n) + prime(n+1), i.e., a(n) = prime(n) + prime(n+1) - a(n-1) generates sequence with initial value a(1)=4. - _Labos Elemer_, Apr 24 2003; corrected by _Dean Hickerson_, Apr 27 2003
%F a(n) = A000040(n+1) - A033999(n+1). - _Juri-Stepan Gerasimov_, Sep 10 2009
%e a(4) + a(3) = 10 + 8 = 18 = prime(4) + prime(5) = 7 + 11.
%t a[1]=4; a[n_] := a[n]=Prime[n]+Prime[n+1]-a[n-1]
%t Total/@Partition[Riffle[Prime[Range[2,60]],{1,-1}],2] (* _Harvey P. Dale_, May 19 2011 *)
%Y Cf. A000040, A033999.
%K nonn,easy
%O 1,1
%A _Mohammad K. Azarian_
%E More terms from _Erich Friedman_
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