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a(1) = 3; thereafter a(n+1) = a(n) + nextprime(a(n)) - prevprime(a(n)).
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%I #14 Oct 13 2024 12:15:11

%S 3,6,8,12,14,18,20,24,30,32,38,42,44,48,54,60,62,68,72,74,80,84,90,98,

%T 102,104,108,110,114,128,132,138,140,150,152,158,164,168,174,180,182,

%U 192,194,198,200,212,224,228,230,234,240,242,252,258,264,270,272,278

%N a(1) = 3; thereafter a(n+1) = a(n) + nextprime(a(n)) - prevprime(a(n)).

%C Essentially the same as A008864. [From _R. J. Mathar_, Oct 28 2008]

%C Only the first term is prime, the rest are even, and between any pair of adjacent terms a(n) and a(n+1), there is just one prime, namely prime(n+2). - _David James Sycamore_, Dec 07 2018

%H Harvey P. Dale, <a href="/A135731/b135731.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n+1) = a(n) + A001223(n+1) for n>1. - _David James Sycamore_, Dec 07 2018

%e a(1) = 3, so a(2) = 3 + (5-2) = 6,

%e a(3) = 6 + (7-5) = 8,

%e a(4) = 8 + (11-7) = 12; etc.

%t NestList[#+NextPrime[#]-NextPrime[#,-1]&,3,60] (* _Harvey P. Dale_, Oct 13 2024 *)

%Y Cf. A001223, A008864, A135732.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Nov 26 2007

%E Definition corrected and entry revised by _David James Sycamore_, Dec 07 2018