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Numbers k such that the k-th prime number is not a Chen prime.
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%I #11 Oct 19 2021 21:32:54

%S 14,18,21,22,25,27,36,38,40,44,48,50,53,58,59,61,65,67,70,73,74,76,78,

%T 82,84,85,88,90,99,101,108,110,111,112,114,117,121,122,125,127,129,

%U 130,131,134,137,143,147,149,153,155,158,163,168,170

%N Numbers k such that the k-th prime number is not a Chen prime.

%H Amiram Eldar, <a href="/A118499/b118499.txt">Table of n, a(n) for n = 1..10000</a>

%e 97 is the 25th prime number but not a Chen prime since 99 = 3*3*11, therefore 25 is in the sequence.

%p ts_inde_nonchen:= proc(n) local i, ans, inde; ans:=[ ]: inde := 0; for i from 1 to n do if ( isprime(i) = 'true') then inde:=inde+1: if (isprime(i+2) = 'false' and numtheory[bigomega](i+2) <> 2) then ans:=[ op(ans), inde ] fi fi od: return ans end: ts_inde_nonchen(2000);

%t Select[Range[180],Sum[FactorInteger[Prime[ # ]+2][[i,2]],{i,1,Length[ FactorInteger[Prime[ # ] + 2]]}] > 2 &]

%o (PARI) isok(k) = (bigomega(prime(k)+2) > 2); \\ _Michel Marcus_, Oct 19 2021

%Y Cf. A102540, A109611.

%K nonn

%O 1,1

%A _Jani Melik_, May 05 2006

%E Edited by _Stefan Steinerberger_, Jul 19 2007