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

1,1

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 A384081 A372046

Adjacent sequences: A235162 A235163 A235164 * A235166 A235167 A235168

Keyword

nonn

Author

Robin Garcia, Jan 04 2014

Status

approved