A234847 Primes which are sum of the first k composite numbers and such that the sum of the first k+1 composites is also prime.

997, 1049, 1709, 2137, 2953, 3889, 3989, 28643, 43451, 121937, 189239, 225077, 662843, 785303, 860143, 874351, 959209, 1026229, 1051151, 1271687, 1285507, 1772297, 2525801, 2834413, 2865199, 3456053, 3484361, 3538477, 4402241, 4762267, 8240539, 11557543, 15774301

Offset: 1

Author

Robin Garcia, Dec 31 2013

Keywords

• nonn

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A053782

Programs

Mathematica

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 *)

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,", "))))