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 A235165 Primes which are sum of the first k consecutive composite numbers and such that the sum of the first consecutive k+1 composites and the sum of the first k+2 consecutive composites are also prime. 2
 997, 3889, 320375057, 423704707, 3431156159, 11650632419, 15909713927, 16906981181, 18170097067, 19703643541, 25534764667, 65405464363, 89483860811, 96873744973, 157599307213, 161983109531, 250812627893, 255555662521, 304165468751, 506667567067, 563313151277, 641930941499, 719915546257, 755132545199, 988899991367, 1002877111091, 1013997492671 (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 997 + 52 = 1049 is prime and 1049 + 54 = 1103 is prime. But 1103 + 55 is even and thus not prime. MATHEMATICA Select[Partition[Accumulate[Select[Range[20*10^6], CompositeQ]], 3, 1], AllTrue[ #, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 30 2017 *) PROG (PARI) i=0; b=0; for( a=2, 2*10^6, if( !isprime(a) , i=i+1; b=b+a; if(( isprime(b) & isprime(b+a+1) &isprime(a+2)& isprime(b+2*a+4))||(isprime(b)&isprime(a+1)&isprime(b+a+2)&isprime(a+3)&isprime(b+2*a+6)), print1(b, ", ")))) CROSSREFS Cf. A053782, A234847. Sequence in context: A091362 A244546 A091365 * A259505 A317594 A226752 Adjacent sequences:  A235162 A235163 A235164 * A235166 A235167 A235168 KEYWORD nonn AUTHOR Robin Garcia, Jan 04 2014 STATUS approved

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Last modified May 15 06:18 EDT 2021. Contains 343909 sequences. (Running on oeis4.)