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.
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
Offset: 1
Keywords
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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 *)
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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,", "))))