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Semiprimes that are the sum of 10 consecutive primes.
1

%I #13 Sep 06 2014 20:44:17

%S 129,158,382,1114,1546,2374,2582,3446,3578,6218,6826,7978,8266,9298,

%T 9382,10202,12946,14002,15178,15406,15766,16382,16466,17282,17362,

%U 18374,18838,19226,19606,23878,24074,25154,25642,26206,29782,30034,30638,32902,33526,34862,34934,35678,35978,36602

%N Semiprimes that are the sum of 10 consecutive primes.

%C Or, semiprimes in A127337 (Numbers that are the sum of 10 consecutive primes).

%C a(1) = 3*43, all other terms are of the form 2*prime.

%H Harvey P. Dale, <a href="/A185347/b185347.txt">Table of n, a(n) for n = 1..1000</a>

%t (* First run the program for A109611 to define semiPrimeQ *) Select[Table[Plus@@Prime[Range[n, n + 9]], {n, 500}], semiPrimeQ] (* _Alonso del Arte_, Feb 15 2011 *)

%t Select[Total/@Partition[Prime[Range[600]],10,1],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Sep 06 2014 *)

%o (PARI) {s=129;for(n=1,2000,if(2==bigomega(s),

%o print1(s", ")); s=s-prime(n)+prime(n+10))} // Zak Seidov, Feb 15 2011

%Y Cf. A127337.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 15 2011