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a(0) = 6; thereafter a(n) = a(n-1) + prime(n) if prime(n) > a(n-1), otherwise a(n) = a(n-1) - prime(n).
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%I #20 Aug 31 2019 23:45:12

%S 6,4,1,6,13,2,15,32,13,36,7,38,1,42,85,38,91,32,93,26,97,24,103,20,

%T 109,12,113,10,117,8,121,248,117,254,115,264,113,270,107,274,101,280,

%U 99,290,97,294,95,306,83,310,81,314,75,316,65,322,59,328,57,334,53,336,43,350,39,352

%N a(0) = 6; thereafter a(n) = a(n-1) + prime(n) if prime(n) > a(n-1), otherwise a(n) = a(n-1) - prime(n).

%C _Hugo van der Sanden_ asks if this ever reaches 0. He finds that a(n) > 0 for n < 5*10^10. Probabilistic arguments suggest it will never reach 0.

%D Hugo van der Sanden, Posting to Sequence Fans Mailing List, Aug 28 2019

%H N. J. A. Sloane, <a href="/A309222/b309222.txt">Table of n, a(n) for n = 0..20000</a>

%Y If we start with 0 or 1 instead of 6 we get A008348, A022837.

%Y Similar in spirit to A008344, and has a similar graph.

%K nonn,look

%O 0,1

%A _N. J. A. Sloane_, Aug 29 2019