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a(n) = c(0)*p(0) + ... + c(n)*p(n), where c(i) = 1 if a(i-1) < p(i) and c(i) = -1 if a(i-1) >= p(i) (p(0) = 1, p(i) = prime(i)).
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%I #29 Sep 05 2019 14:31:51

%S 1,3,0,5,12,1,14,31,12,35,6,37,0,41,84,37,90,31,92,25,96,23,102,19,

%T 108,11,112,9,116,7,120,247,116,253,114,263,112,269,106,273,100,279,

%U 98,289,96,293,94,305,82,309,80,313,74,315,64,321,58,327,56,333,52,335

%N a(n) = c(0)*p(0) + ... + c(n)*p(n), where c(i) = 1 if a(i-1) < p(i) and c(i) = -1 if a(i-1) >= p(i) (p(0) = 1, p(i) = prime(i)).

%C Alternative definition: a(0)=1; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n). Cf. A008348. - _N. J. A. Sloane_, Aug 31 2019

%H Seiichi Manyama, <a href="/A022837/b022837.txt">Table of n, a(n) for n = 0..10000</a>

%e From _Seiichi Manyama_, Sep 05 2019: (Start)

%e a(0) = 1.

%e a(1) = 1 + 2 = 3.

%e a(2) = 1 + 2 - 3 = 0.

%e a(3) = 1 + 2 - 3 + 5 = 5.

%e a(4) = 1 + 2 - 3 + 5 + 7 = 12.

%e a(5) = 1 + 2 - 3 + 5 + 7 - 11 = 1. (End)

%Y Cf. A000040, A008348, A008578.

%Y See also A324787, A324788, A324789, A324790.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E Missing a(46)=94 inserted and name corrected by _Sean A. Irvine_, May 21 2019