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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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.

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 *)

PROG

(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, ", "))))

CROSSREFS

Cf. A053782

Sequence in context: A267119 A210315 A182694 * A057698 A106763 A247122

Adjacent sequences:  A234844 A234845 A234846 * A234848 A234849 A234850

KEYWORD

nonn

AUTHOR

Robin Garcia, Dec 31 2013

STATUS

approved

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Last modified October 17 14:19 EDT 2019. Contains 328113 sequences. (Running on oeis4.)