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%I #7 Aug 12 2014 08:36:12
%S 997,1049,1709,2137,2953,3889,3989,28643,43451,121937,189239,225077,
%T 662843,785303,860143,874351,959209,1026229,1051151,1271687,1285507,
%U 1772297,2525801,2834413,2865199,3456053,3484361,3538477,4402241,4762267,8240539,11557543,15774301
%N Primes which are sum of the first k composite numbers and such that the sum of the first k+1 composites is also prime.
%H Harvey P. Dale, <a href="/A234847/b234847.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)= 997 is prime and sum of the first 35 composites from 4 to 51. And the sum of the first 36 composites is 1049 and is also prime.
%t Transpose[Select[Partition[Accumulate[Select[Range[ 10000], CompositeQ]],2,1],AllTrue[ #,PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 12 2014 *)
%o (PARI) i=0; b=0; for( a=2, 6000, if( !isprime(a) ,i=i+1; b=b+a; if(( isprime(b) & isprime(b+a+1)& !isprime(a+1)) || (isprime(b) & isprime(b+a+2) & isprime(a+1)), print1(b,", "))))
%Y Cf. A053782
%K nonn
%O 1,1
%A _Robin Garcia_, Dec 31 2013
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